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{"work":{"id":102261870,"created_at":"2023-05-23T20:02:50.783-07:00","from_world_paper_id":234351182,"updated_at":"2024-11-23T23:27:33.698-08:00","_data":{"grobid_abstract":"In this paper, we present concepts of pre γp-open sets and pre γpclosures of a subset in a topological space, where γp is an operation on the family of all preopen sets of the topological space, and study some topological properties on them. As its application, we introduce the concept of pre γp-Ti spaces (i = 0, 1/2, 1, 2) and study some properties of these spaces.","publication_date":"2008,7,1","publication_name":"Scientiae Mathematicae Japonicae","grobid_abstract_attachment_id":"102576125"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"On Operation-Preopen Sets in Topological Spaces","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [270973589]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; 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":102576125,"attachmentType":"pdf"}"><img alt="First page of “On Operation-Preopen Sets in Topological Spaces”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/102576125/mini_magick20230524-1-7bcc2e.png?1684897467" /><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 Operation-Preopen 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="270973589" href="https://independent.academia.edu/CUONGXUAN11"><img alt="Profile image of CUONG XUAN" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/270973589/121283180/110614726/s65_cuong.xuan.png" />CUONG XUAN</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2008, Scientiae Mathematicae Japonicae</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">20 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 = 102261870; 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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">In this paper, we present concepts of pre γp-open sets and pre γpclosures of a subset in a topological space, where γp is an operation on the family of all preopen sets of the topological space, and study some topological properties on them. As its application, we introduce the concept of pre γp-Ti spaces (i = 0, 1/2, 1, 2) and study some properties of these 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":102576125,"attachmentType":"pdf","workUrl":"https://www.academia.edu/102261870/On_Operation_Preopen_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":102576125,"attachmentType":"pdf","workUrl":"https://www.academia.edu/102261870/On_Operation_Preopen_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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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="1" data-entity-id="27292122" 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/27292122/Some_More_Results_on_Preopen_Sets_in_Topology">Some More Results on 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 1982 , A.S.Mashhour et al [2] have defined the notion of preopen sets. The notion of preopen sets play a significant role in general topology. Preopen sets are also called nearly open and locally dense sets by several authors in the literature. They are not only important in the context of covering properties and decompositions of continuity but also in functional analysis in the context of open mapping theorems and closed graph theorems. The concepts of preclosure and preinterior of a set are also due to A.S.Mashhour et al [1]&[3]. 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js-wsj-grid-card" data-collection-position="2" data-entity-id="71722500" 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/71722500/Characterizations_of_PRE_R0_and_PRE_R1_Topological_Spaces">Characterizations of PRE-R0 and PRE-R1 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--metadata ds2-5-body-xs">2000</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper we introduce two new classes of topological spaces called pre-R0 and pre-R1 spaces in terms of the concept of preopen sets and investigate some of their fundamental 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":"Characterizations of PRE-R0 and PRE-R1 Topological Spaces","attachmentId":80948229,"attachmentType":"pdf","work_url":"https://www.academia.edu/71722500/Characterizations_of_PRE_R0_and_PRE_R1_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/71722500/Characterizations_of_PRE_R0_and_PRE_R1_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="3" data-entity-id="85208900" data-sort-order="default"><a 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sets","attachmentId":89977532,"attachmentType":"pdf","work_url":"https://www.academia.edu/85208900/On_some_topological_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/85208900/On_some_topological_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="4" 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 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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="5" data-entity-id="50516802" 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/50516802/Some_applications_of_generalized_open_sets_via_operations">Some applications of generalized open sets via operations</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="49527792" href="https://zakho.academia.edu/BaravanAsaad">Baravan Asaad</a></div><p class="ds-related-work--metadata ds2-5-body-xs">New Trends in Mathematical Science</p><p class="ds-related-work--abstract ds2-5-body-sm">This paper introduces the concept of an operation on τ g. Using this operation, we define the concept of g-γ-open sets, and study some of their related notions. Also, we introduce the concept of gγ-generalized closed sets and then investigate some of its properties. Furthermore, we introduce and investigate g-γ-T i spaces (i ∈ {0, 1 2 , 1, 2}) and g-(γ, β)-continuous functions by utilizing the operation γ on τ g. Finally, some basic properties of functions with g-β-closed graphs have been obtained.</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 generalized open sets via operations","attachmentId":68470992,"attachmentType":"pdf","work_url":"https://www.academia.edu/50516802/Some_applications_of_generalized_open_sets_via_operations","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/50516802/Some_applications_of_generalized_open_sets_via_operations"><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="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="7" data-entity-id="126293616" 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/126293616/P_Jeyanthi_P_Nalayini_and_T_Noiri_Pre_regular_sp_open_sets_in_topological_spaces_CUBO_A_Mathematical_JournalVol_20_1_2018_31_39">P. 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. Nalayini and T.Noiri, Pre- regular sp- open sets in topological spaces, CUBO A Mathematical JournalVol.20, (1)( 2018),. 31–39","attachmentId":120193138,"attachmentType":"pdf","work_url":"https://www.academia.edu/126293616/P_Jeyanthi_P_Nalayini_and_T_Noiri_Pre_regular_sp_open_sets_in_topological_spaces_CUBO_A_Mathematical_JournalVol_20_1_2018_31_39","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/126293616/P_Jeyanthi_P_Nalayini_and_T_Noiri_Pre_regular_sp_open_sets_in_topological_spaces_CUBO_A_Mathematical_JournalVol_20_1_2018_31_39"><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="10396900" 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/10396900/Journal_of_College_of_Education_for_Pure_Sciences_Open_closed_and_continuous_function_in_bi_pre_supra_topological_space">Journal of College of Education for Pure Sciences Open, closed and continuous function in bi-pre-supra topological space</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="25559761" href="https://independent.academia.edu/AbduAbdu4">Abdu Abdu</a></div><p class="ds-related-work--abstract ds2-5-body-sm">In this paper we construction a new space called bi-pre-supra topological space . Many concepts ( , )-open set ,( , * )-open set , bi-open set ) were introduced . At last through this paper we introduced a new class of functions (open , closed and continuous ) in bi-pre-supra topological space . We study and investigate some properties and characterization of above concepts . ‫الملخص‬ : ‫عليو‬ ‫اطلق‬ ‫الفضاءات‬ ‫من‬ ‫جذيذ‬ ‫نوع‬ ‫قذمنا‬ ‫البحث‬ ‫ىذا‬ ‫في‬ bi-pre-supra topological space) ) ‫حيث‬ ‫الذوال‬ ‫من‬ ‫جذيذ‬ ‫نوع‬ ‫تقذيم‬ ‫تم‬ ‫كما‬ ‫المزدوجو‬ ‫المفتوحو‬ ‫المجموعو‬ ‫مثل‬ ‫الفضاء‬ ‫ىذا‬ ‫في‬ ‫مفاىيم‬ ‫مجموعة‬ ‫على‬ ‫التعزف‬ ‫تم‬ ( ‫مفتوحو‬ , ‫ومستمزه‬ ‫مغلقو‬ ) ‫السابقة‬ ‫للمفاىيم‬ ‫والصفات‬ ‫الخواص‬ ‫بعض‬ ‫دراسة‬ ‫تم‬ ‫كما‬ ‫الجذيذ‬ ‫الفضاء‬ ‫ىذا‬ ‫في‬ .</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":"Journal of College of Education for Pure Sciences Open, closed and continuous function in bi-pre-supra topological space","attachmentId":36453149,"attachmentType":"pdf","work_url":"https://www.academia.edu/10396900/Journal_of_College_of_Education_for_Pure_Sciences_Open_closed_and_continuous_function_in_bi_pre_supra_topological_space","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/10396900/Journal_of_College_of_Education_for_Pure_Sciences_Open_closed_and_continuous_function_in_bi_pre_supra_topological_space"><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="88406534" 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/88406534/Operation_approaches_on_%CE%B1_%CE%B3_I_open_sets_and_%CE%B1_%CE%B3_I_continuous_functions_in_topological_spaces">Operation approaches on α-γ-I-open sets and α-γ-I-continuous functions 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="63135298" href="https://independent.academia.edu/AElMaghrabi">A. I El-Maghrabi</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of the Egyptian Mathematical Society, 2014</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper, the notion of a-c-I-open sets in a topological space together with its corresponding interior and closure operators are introduced. Further, the concept of a-c-I-continuous functions and a-c-I-open functions are introduced and some of their basic properties are studied.</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":"Operation approaches on α-γ-I-open sets and α-γ-I-continuous functions in topological spaces","attachmentId":92384026,"attachmentType":"pdf","work_url":"https://www.academia.edu/88406534/Operation_approaches_on_%CE%B1_%CE%B3_I_open_sets_and_%CE%B1_%CE%B3_I_continuous_functions_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/88406534/Operation_approaches_on_%CE%B1_%CE%B3_I_open_sets_and_%CE%B1_%CE%B3_I_continuous_functions_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></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":102576125,"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":102576125,"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_102576125" 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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