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window.loswp.shouldDetectTimezone = true; window.loswp.shouldShowBulkDownload = true; window.loswp.showSignupCaptcha = false window.loswp.willEdgeCache = false; window.loswp.work = {"work":{"id":50437514,"created_at":"2021-07-31T05:14:38.839-07:00","from_world_paper_id":171315383,"updated_at":"2025-02-02T14:53:43.672-08:00","_data":{"ai_title_tag":"Properties of γ*-Semi-Open Sets and Functions","grobid_abstract":"In this paper, we continue studying the properties of γ *-semi-open sets in topological spaces introduced by S. Hussain, B. Ahmad and T. Noiri[8]. We also introduce and discuss the γ *-semi-continuous functions which generalize semi-continuous functions defined by N. Levine [10]. Keywords. γ-closed (open) sets, γ-closure , γ *-semi-closed (open) sets, γ *-semi-closure, γ-regular, γ *-semi-interior, γ-semi-continuous functions, γ-semi-open (closed) mappings.","grobid_abstract_attachment_id":"68426386"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"$\\gamma^{*}$-semi-open Sets in Topological Spaces-II","broadcastable":false,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [133663907]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "control"; window.loswp.useOptimizedScribd4genScript = false; window.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon'; window.userInChina = "false";</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":68426386,"attachmentType":"pdf"}"><img alt="First page of “$\gamma^{*}$-semi-open Sets in Topological Spaces-II”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/68426386/mini_magick20210731-24966-19z5gzw.png?1627733798" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">$\gamma^{*}$-semi-open Sets in Topological Spaces-II</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="133663907" href="https://independent.academia.edu/SabirHussain128"><img alt="Profile image of Sabir Hussain" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/133663907/166797139/156718782/s65_sabir.hussain.jpeg" />Sabir Hussain</a></div><div class="ds-work-card--detail"><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">12 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 50437514; const worksViewsPath = "/v0/works/views?subdomain_param=api&work_ids%5B%5D=50437514"; const getWorkViews = async (workId) => { const response = await fetch(worksViewsPath); if (!response.ok) { throw new Error('Failed to load work views'); } const data = await response.json(); return data.views[workId]; }; // Get the view count for the work - we send this immediately rather than waiting for // the DOM to load, so it can be available as soon as possible (but without holding up // the backend or other resource requests, because it's a bit expensive and not critical). const viewCount = await getWorkViews(workId); const updateViewCount = (viewCount) => { try { const viewCountNumber = parseInt(viewCount, 10); if (viewCountNumber === 0) { // Remove the whole views element if there are zero views. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); return; } const commaizedViewCount = viewCountNumber.toLocaleString(); const viewCountBody = document.getElementById('work-metadata-view-count'); if (!viewCountBody) { throw new Error('Failed to find work views element'); } viewCountBody.textContent = `${commaizedViewCount} views`; } catch (error) { // Remove the whole views element if there was some issue parsing. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); throw new Error(`Failed to parse view count: ${viewCount}`, error); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">In this paper, we continue studying the properties of γ *-semi-open sets in topological spaces introduced by S. Hussain, B. Ahmad and T. Noiri[8]. We also introduce and discuss the γ *-semi-continuous functions which generalize semi-continuous functions defined by N. Levine [10]. Keywords. γ-closed (open) sets, γ-closure , γ *-semi-closed (open) sets, γ *-semi-closure, γ-regular, γ *-semi-interior, γ-semi-continuous functions, γ-semi-open (closed) mappings.</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":68426386,"attachmentType":"pdf","workUrl":"https://www.academia.edu/50437514/_gamma_semi_open_Sets_in_Topological_Spaces_II"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":68426386,"attachmentType":"pdf","workUrl":"https://www.academia.edu/50437514/_gamma_semi_open_Sets_in_Topological_Spaces_II"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div><div class="ds-signup-banner-trigger-container"><div class="ds-signup-banner-trigger ds-signup-banner-trigger-control"></div></div><div class="ds-signup-banner ds-signup-banner-control"><div id="ds-signup-banner-close-button"><button class="ds2-5-button ds2-5-button--secondary ds2-5-button--inverse"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">close</span></button></div><div class="ds-signup-banner-ctas"><img src="//a.academia-assets.com/images/academia-logo-capital-white.svg" /><h4 class="ds2-5-heading-serif-sm">Sign up for access to the world's latest research</h4><button class="ds2-5-button ds2-5-button--inverse ds2-5-button--full-width js-swp-download-button" data-signup-modal="{"location":"signup-banner"}">Sign up for free<span class="material-symbols-outlined" style="font-size: 20px" translate="no">arrow_forward</span></button></div><div class="ds-signup-banner-divider"></div><div class="ds-signup-banner-reasons"><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Get notified about relevant papers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Save papers to use in your research</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Join the discussion with peers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Track your impact</span></div></div></div><script>(() => { // Set up signup banner show/hide behavior: // 1. 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In the spirit of Latif (1999), Min (2002) used the idea of semi-convergence of filters to introduce a new class of sets, called γ − open sets, and the notions of γ − closure, γ − interior and γ − continuity and investigated some properties. In this paper we introduce γ − continuous, γ − irresolute, γ − open, γ − closed, pre − γ − open and pre − γ − closed mappings and investigate properties and characterizations of these new types of mappings.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Characterizations of Mappings in γ-Open Sets","attachmentId":78401205,"attachmentType":"pdf","work_url":"https://www.academia.edu/67663147/Characterizations_of_Mappings_in_%CE%B3_Open_Sets","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/67663147/Characterizations_of_Mappings_in_%CE%B3_Open_Sets"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="96554054" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/96554054/Characterizations_and_applications_of_%CE%B3_open_sets">Characterizations and applications of γ-open sets</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="91741988" href="https://independent.academia.edu/RMLatif">R. M. Latif</a></div><p class="ds-related-work--abstract ds2-5-body-sm">The notion of semi-convergence of filters was introduced by the author in [Math. J. Okayama Univ. 41, 103–109 (1999; Zbl 0970.54003)] when investigating some characterizations related to semi-open continuous functions. W. K. Min [Int. J. Math. Math. Sci. 31, 177–181 (2002; Zbl 0993.54015)] used the idea of semi-convergence of filters to introduce a new class of sets, called γ-open sets, and the notions of γ-closure, γ-interior and γ-continuity and to investigate some properties. In this paper we continue to explore further properties of these notions as well as characterizations of γ-open sets. We also introduce and study topological properties of γ-derived, γ-border, γ-frontier, and γ-exterior of a set using the concept of γ-open sets.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Characterizations and applications of γ-open sets","attachmentId":98420636,"attachmentType":"pdf","work_url":"https://www.academia.edu/96554054/Characterizations_and_applications_of_%CE%B3_open_sets","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/96554054/Characterizations_and_applications_of_%CE%B3_open_sets"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="4882827" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/4882827/On_Semi_Open_Sets_and_Semi_Continuous_Functions">On Semi--Open Sets and Semi--Continuous Functions</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="2594470" href="https://independent.academia.edu/iosrjournals">IOSR Journals</a></div><p class="ds-related-work--abstract ds2-5-body-sm">We study the concepts of semi--open sets and semi--continuous functions introduced in [13] and some properties of the functions. Also we introduce notion of semi--open and semi--closed functions.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On Semi--Open Sets and Semi--Continuous Functions","attachmentId":32154743,"attachmentType":"pdf","work_url":"https://www.academia.edu/4882827/On_Semi_Open_Sets_and_Semi_Continuous_Functions","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/4882827/On_Semi_Open_Sets_and_Semi_Continuous_Functions"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="32155617" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/32155617/Some_properties_of_%CE%B8_%CE%B8_%CE%B8_%CE%B8_semi_open_sets_in_topological_spaces">Some properties of θ θ θ θ * -semi-open sets in topological spaces</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="8373275" href="https://taif.academia.edu/AliMubarki">Ali Mubarki</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="63135298" href="https://independent.academia.edu/AElMaghrabi">A. I El-Maghrabi</a></div><p class="ds-related-work--abstract ds2-5-body-sm">The aim of this paper is to introduce and study the notion of θ *-semi-open sets and θ *-semi-continuous functions. Some characterizations and properties of these notions are presented. (2000)</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Some properties of θ θ θ θ * -semi-open sets in topological spaces","attachmentId":52393971,"attachmentType":"pdf","work_url":"https://www.academia.edu/32155617/Some_properties_of_%CE%B8_%CE%B8_%CE%B8_%CE%B8_semi_open_sets_in_topological_spaces","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/32155617/Some_properties_of_%CE%B8_%CE%B8_%CE%B8_%CE%B8_semi_open_sets_in_topological_spaces"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="4" data-entity-id="62841292" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/62841292/On_Semi_%CE%B4_Open_Sets_in_Topological_Spaces">On Semi*δ- Open Sets in Topological Spaces</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="37922294" href="https://independent.academia.edu/piousmissier">pious missier</a></div><p class="ds-related-work--metadata ds2-5-body-xs">IOSR Journal of Mathematics</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper, we introduce a new class of sets, namely semi*δ-open sets, using δ-open sets and the generalized closure operator. We find characterizations of semi*δ-open sets. We also define the semi*δ-interior of a subset. Further, we study some fundamental properties of semi*δ-open sets and semi*δ-interior.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On Semi*δ- Open Sets in Topological Spaces","attachmentId":75479214,"attachmentType":"pdf","work_url":"https://www.academia.edu/62841292/On_Semi_%CE%B4_Open_Sets_in_Topological_Spaces","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/62841292/On_Semi_%CE%B4_Open_Sets_in_Topological_Spaces"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="27323780" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/27323780/Some_Generalized_Continuous_Functions_via_Generalized_Semipre_Open_Sets">Some Generalized Continuous Functions via Generalized Semipre-Open Sets</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="2641280" href="https://technology-iraq.academia.edu/GovindappaNavalagi">Govindappa Navalagi</a></div><p class="ds-related-work--abstract ds2-5-body-sm">In the year 1986, D. Andrijevic introduced and studied the concepts of semipreopen sets, semipreclosed sets, semipreinterior operator and semipreclosure operator. Since then many authors have been studied these sets and their operators. In the year 1970, N. Levine had generalized the concept of closed sets and open sets to generalized closed (in brief, g-closed) sets and generalized open (in brief, g-open) sets in topology for the first time. Then, in the year 1995 Dontchev has generalized semipreopen sets and semipreclosed to generalized semipreopen (in brief, gsp-open) sets and generalized semipreclosed (in brief, gsp-closed) sets. Also, Dontchev in his paper has studied the concepts of gsp-continuous functions and gsp-irresolute functions. The aim of this paper is to study some more properties of gsp-continuous functions and gsp-irresolute functions and also introduce and study some allied continuous functions in terms of gsp-open sets and gsp-closed sets in topology. 2010 M.S.C....</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Some Generalized Continuous Functions via Generalized Semipre-Open Sets","attachmentId":47580436,"attachmentType":"pdf","work_url":"https://www.academia.edu/27323780/Some_Generalized_Continuous_Functions_via_Generalized_Semipre_Open_Sets","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/27323780/Some_Generalized_Continuous_Functions_via_Generalized_Semipre_Open_Sets"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="126220223" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/126220223/On_New_Types_of_Sets_Via_%CE%B3_open_Sets_in_a_Topological_Spaces">On New Types of Sets Via γ-open Sets in (𝑎)Topological Spaces</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="327841696" href="https://independent.academia.edu/SheetalLuthra1">Sheetal Luthra</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Cubo (Temuco), 2018</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper, we introduced the notion of γ-semi-open sets and γ-P-semi-open sets in (a)topological spaces which is a set equipped with countable number of topologies. Several properties of these notions are discussed. RESUMEN En este artículo, introducimos la noción de conjuntos γ-semi-abiertos y conjuntos γ-Psemi-abiertos en espacios (a)topológicos, el cual es un conjunto dotado con una cantidad numerable de topologías. Discutimos diversas propiedades de estas nociones.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On New Types of Sets Via γ-open Sets in (𝑎)Topological Spaces","attachmentId":120130496,"attachmentType":"pdf","work_url":"https://www.academia.edu/126220223/On_New_Types_of_Sets_Via_%CE%B3_open_Sets_in_a_Topological_Spaces","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/126220223/On_New_Types_of_Sets_Via_%CE%B3_open_Sets_in_a_Topological_Spaces"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="64623336" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/64623336/%CE%93_open_Function_and_%CE%93_closed_Functions">Γ−open Function and Γ−closed Functions</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="50661863" href="https://independent.academia.edu/qefseregjonbalaj">qefsere gjonbalaj</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2019</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper we define two types of functions of topological spaces: γ−open functions and γ−closed functions. In addition, we examine the relation of these functions among themselves and their relation with γ−continuous functions. In the following, we study some properties of γ−open and γ−closed functions. AMS Subject Classification: 54A05, 54A10, 54D10</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Γ−open Function and Γ−closed Functions","attachmentId":76573239,"attachmentType":"pdf","work_url":"https://www.academia.edu/64623336/%CE%93_open_Function_and_%CE%93_closed_Functions","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/64623336/%CE%93_open_Function_and_%CE%93_closed_Functions"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="27292101" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/27292101/Some_Allied_Open_Functions_via_Semipreopen_and_Preopen_Sets_in_Topology">Some Allied Open Functions via Semipreopen and Preopen Sets in Topology</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="5323318" href="https://independent.academia.edu/Navalagi">Govindappa Navalagi</a></div><p class="ds-related-work--abstract ds2-5-body-sm">In 1986, D.Andrijevic had defined and studied the concepts of semipreopen sets and semipreclosed sets in topology. In 2002, Navalagi has defined and studied classes of various continuous functions, open functions and closed functions in between topological spaces using semipreopen sets and semipreclosed sets. In this paper, we define and study some new classes of functions called p-semipreopen functions and contra-p-semipreopen functions using semipreopen sets, preopen sets. Also, we characterize their basic properties. Mathematics Subject Classification 2000: 54 A05, 54 C08.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Some Allied Open Functions via Semipreopen and Preopen Sets in Topology","attachmentId":47551363,"attachmentType":"pdf","work_url":"https://www.academia.edu/27292101/Some_Allied_Open_Functions_via_Semipreopen_and_Preopen_Sets_in_Topology","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/27292101/Some_Allied_Open_Functions_via_Semipreopen_and_Preopen_Sets_in_Topology"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="23256382" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/23256382/_and_952_GENERALIZED_Semi_Open_and_and_952_GENERALIZED_Semi_Closed_Functions">&#952;-GENERALIZED Semi-Open and &#952;-GENERALIZED Semi-Closed Functions</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="45126961" href="https://kletech.academia.edu/MdHanifPage">Md. Hanif Page</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Proyecciones (Antofagasta), 2009</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper, we introduce and study the notions of θ-generalizedsemi-open function, θ-generalized-semi-closed function,pre-θ-generalizedsemi-open function,pre-θ-generalized-semi-closed function, contra preθ-generalized-semi-open,contra pre-θ-generalized-semi-closed function and θ-generlized-sem-homeomorphism in topological spaces and study their properties.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"\u0026#952;-GENERALIZED Semi-Open and \u0026#952;-GENERALIZED Semi-Closed Functions","attachmentId":43735025,"attachmentType":"pdf","work_url":"https://www.academia.edu/23256382/_and_952_GENERALIZED_Semi_Open_and_and_952_GENERALIZED_Semi_Closed_Functions","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/23256382/_and_952_GENERALIZED_Semi_Open_and_and_952_GENERALIZED_Semi_Closed_Functions"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":68426386,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":68426386,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_68426386" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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