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{"work":{"id":86217472,"created_at":"2022-09-06T01:15:57.312-07:00","from_world_paper_id":214461683,"updated_at":"2024-11-25T15:57:52.908-08:00","_data":{"publisher":"Kirkuk University","grobid_abstract":"The aim of this paper is to introduce and study some properties of pre--open sets,and study a new class of spaces, called  p-regular space. Determine some properties of  p-regularity and compare with other types of regular spaces.","publication_date":"2007,,","publication_name":"Kirkuk University Journal-Scientific Studies","grobid_abstract_attachment_id":"90721711"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"On p-open sets in topological spaces","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [7209569]; 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":90721711,"attachmentType":"pdf"}"><img alt="First page of “On p-open sets in topological spaces”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/90721711/mini_magick20220906-1-i5kf5m.png?1662456038" /><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">On p-open sets in topological spaces</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="7209569" href="https://independent.academia.edu/NehmatAhmed"><img alt="Profile image of Nehmat Ahmed" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/7209569/5349116/6108278/s65_nehmat.ahmed.jpg_oh_19d4c0ef71e0627916fe5a341d552724_oe_54b95cf8___gda___1424806953_054d31aa8689d66258d0b75f9b382718" />Nehmat Ahmed</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2007, Kirkuk University Journal-Scientific Studies</p><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">8 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 = 86217472; 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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">The aim of this paper is to introduce and study some properties of pre--open sets,and study a new class of spaces, called  p-regular space. Determine some properties of  p-regularity and compare with other types of regular spaces.</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":90721711,"attachmentType":"pdf","workUrl":"https://www.academia.edu/86217472/On_p_open_sets_in_topological_spaces"}">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":90721711,"attachmentType":"pdf","workUrl":"https://www.academia.edu/86217472/On_p_open_sets_in_topological_spaces"}"><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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Jeyanthi, P. Nalayini and T.Noiri, Pre- regular sp- open sets in topological spaces, CUBO A Mathematical JournalVol.20, (1)( 2018),. 31–39</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="49634263" href="https://tvl.academia.edu/PJeyanthi">P. Jeyanthi</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="86880252" href="https://independent.academia.edu/TNoiri">T. Noiri</a></div><p class="ds-related-work--metadata ds2-5-body-xs">CUBO A Mathematical Journal, 2018</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper, a new class of generalized open sets in a topological space, called preregular sp-open sets, is introduced and studied. This class is contained in the class of semi-preclopen sets and cotains all pre-clopen sets. We obtain decompositions of regular open sets by using pre-regular sp-open sets. RESUMEN En este artículo se introduce y estudia una nueva clase de conjuntos abiertos generalizados en un espacio topológico, llamados conjuntos pre-regulares sp-abiertos. Esa clase está contenida en la clase de conjuntos semi-preclopen y contiene todos los conjuntos pre-clopen. Obtenemos descomposiciones de conjuntos abiertos regulares usando conjuntos pre-regulares sp-abiertos.</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":"P. Jeyanthi, P. 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The relationships among normal, p-normal, -normal, -normal and -normal spaces are investigated. Moreover, we introduced some functions such as g-closed, -g-closed, pre -open. We obtained some characterizations of -normal and -regular spaces, properties of the forms of g-closed functions and preservation theorems for -normal and -regular spaces.</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":"Normal and-Regular Spaces in Topological Spaces","attachmentId":76675721,"attachmentType":"pdf","work_url":"https://www.academia.edu/64817181/Normal_and_Regular_Spaces_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/64817181/Normal_and_Regular_Spaces_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="37070166" 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/37070166/Some_allied_regular_spaces_via_gsp_open_sets_in_topology">Some allied regular spaces via gsp-open 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="2594470" href="https://independent.academia.edu/iosrjournals">IOSR Journals</a></div><p class="ds-related-work--abstract ds2-5-body-sm">In this paper we define and study some allied regular spaces using gsp-open sets and gsp-closed</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 regular spaces via gsp-open sets in topology","attachmentId":57021387,"attachmentType":"pdf","work_url":"https://www.academia.edu/37070166/Some_allied_regular_spaces_via_gsp_open_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/37070166/Some_allied_regular_spaces_via_gsp_open_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="5" data-entity-id="85341416" 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/85341416/Pre_Regular_P_Open_Sets_and_Decompositions_of_Complete_Continuity">Pre-Regular P-Open Sets and Decompositions of Complete Continuity</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="2790607" href="https://independent.academia.edu/PJeyanthi">P. Jeyanthi</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2016</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper, we investigate and characterize pre-regular p-open sets which are defined by Jafari [9] , using the pre-interior and pre-closure operators. By using pre-regular p-open sets, we obtain decompositions of regular open sets and decompositions of complete continuity. It is shown that b-closed sets defined in [17] are equivalent to regular open sets. This fact improves many results obtained in [17].</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":"Pre-Regular P-Open Sets and Decompositions of Complete Continuity","attachmentId":90067121,"attachmentType":"pdf","work_url":"https://www.academia.edu/85341416/Pre_Regular_P_Open_Sets_and_Decompositions_of_Complete_Continuity","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/85341416/Pre_Regular_P_Open_Sets_and_Decompositions_of_Complete_Continuity"><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="23242990" 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/23242990/Some_Applications_of_Preopen_Sets_in_Topological_Spaces">Some Applications of �-Preopen 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="45104431" href="https://independent.academia.edu/SaeidJafari5">Saeid Jafari</a></div><p class="ds-related-work--abstract ds2-5-body-sm">In 1993, Raychaudhuri and Mukherjee introduced the notions of δ-preopen sets and δ-preclosure. In this paper, we introduce some weak separation axioms by utilizing the notions of δ-preopen sets and the δ-preclosure operator.</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 Applications of �-Preopen Sets in Topological Spaces","attachmentId":43726028,"attachmentType":"pdf","work_url":"https://www.academia.edu/23242990/Some_Applications_of_Preopen_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/23242990/Some_Applications_of_Preopen_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="7" data-entity-id="27292123" 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/27292123/On_Some_More_properties_of_generalized_preclosed_sets_in_topological_spaces">On Some More properties of generalized preclosed 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="5323318" href="https://independent.academia.edu/Navalagi">Govindappa Navalagi</a></div><p class="ds-related-work--abstract ds2-5-body-sm">In the year 1982 , A.S.Mashhour et al have defined and studied the concepts of preopen sets and precontinuous functions in topology. Latter in the year 1983, S.N.El-Deeb et al have defined</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 Some More properties of generalized preclosed sets in topological spaces","attachmentId":47551372,"attachmentType":"pdf","work_url":"https://www.academia.edu/27292123/On_Some_More_properties_of_generalized_preclosed_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/27292123/On_Some_More_properties_of_generalized_preclosed_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="8" data-entity-id="126284991" 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/126284991/P_Jeyanthi_P_Nalayini_and_T_Noiri_Pre_regular_p_open_sets_and_decompositions_of_complete_continuity_Jordon_Journal_of_Mathematics_and_Statistics_9_3_2016_227_237">P. Jeyanthi, P. Nalayini and T.Noiri, Pre- regular p-open sets and decompositions of complete continuity, Jordon Journal of Mathematics and Statistics, 9(3)2016,227- 237</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="49634263" href="https://tvl.academia.edu/PJeyanthi">P. Jeyanthi</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Jordon Journal of Mathematics and Statistics,, 2016</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper, we investigate and characterize pre-regular p-open sets which are defined by Jafari [9] , using the pre-interior and pre-closure operators. By using pre-regular p-open sets, we obtain decompositions of regular open sets and decompositions of complete continuity. It is shown that b-closed sets defined in [17] are equivalent to regular open sets. This fact improves many results obtained in [17].</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":"P. Jeyanthi, P. Nalayini and T.Noiri, Pre- regular p-open sets and decompositions of complete continuity, Jordon Journal of Mathematics and Statistics, 9(3)2016,227- 237","attachmentId":120185942,"attachmentType":"pdf","work_url":"https://www.academia.edu/126284991/P_Jeyanthi_P_Nalayini_and_T_Noiri_Pre_regular_p_open_sets_and_decompositions_of_complete_continuity_Jordon_Journal_of_Mathematics_and_Statistics_9_3_2016_227_237","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/126284991/P_Jeyanthi_P_Nalayini_and_T_Noiri_Pre_regular_p_open_sets_and_decompositions_of_complete_continuity_Jordon_Journal_of_Mathematics_and_Statistics_9_3_2016_227_237"><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="80387845" 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/80387845/On_Generalized_Regular_Closed_Sets">On Generalized Regular Closed 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="108379037" href="https://independent.academia.edu/SharmisthaBhattacharya">Sharmistha Bhattacharya</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2010</p><p class="ds-related-work--abstract ds2-5-body-sm">The aim of this paper is to introduce the concept of generalized regular closed sets and study some of its properties . The corresponding topological space formed by the family of these sets is also studied. It may be noted that regular closed set doesn’t forms even a supra topological space. Various researchers had studied the concept of generalized closed sets and regular generalized closed sets earlier. The generalized closed set is properly placed between the generalized regular closed sets and regular generalized closed set. The connection of the topological space formed by the newly defined sets with other topological space are also discussed in this paper and some applications of this newly defined set are also shown. Mathematics Subject Classification: 54A40</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 Generalized Regular Closed Sets","attachmentId":86786096,"attachmentType":"pdf","work_url":"https://www.academia.edu/80387845/On_Generalized_Regular_Closed_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/80387845/On_Generalized_Regular_Closed_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></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":90721711,"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":90721711,"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_90721711" 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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