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multiset local function on an ideal topological space using the the concept of q-neighbourhood in a multiset topological space. Some basic properties of local functions on multisets have been investigated in multiset ideal topological space.","publication_name":"Proyecciones (Antofagasta)","grobid_abstract_attachment_id":"81133880"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Multiset ideal topological spaces and local functions","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [33297539]; 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.loswp.appleClientId = 'edu.academia.applesignon';</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":81133880,"attachmentType":"pdf"}"><img alt="First page of “Multiset ideal topological spaces and local functions”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/81133880/mini_magick20220220-19312-1xzaxie.png?1645424121" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/assets/single_work_splash/adobe.icon-574afd46eb6b03a77a153a647fb47e30546f9215c0ee6a25df597a779717f9ef.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">Multiset ideal topological spaces and local functions</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="33297539" href="https://independent.academia.edu/BinodTripathy"><img alt="Profile image of Binod Tripathy" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/33297539/22573455/21763950/s65_binod.tripathy.jpg" />Binod Tripathy</a></div><p class="ds-work-card--detail ds2-5-body-sm">Proyecciones (Antofagasta)</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":81133880,"attachmentType":"pdf","workUrl":"https://www.academia.edu/72042797/Multiset_ideal_topological_spaces_and_local_functions"}">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":81133880,"attachmentType":"pdf","workUrl":"https://www.academia.edu/72042797/Multiset_ideal_topological_spaces_and_local_functions"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div></div><div data-auto_select="false" data-client_id="331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b" data-doc_id="81133880" data-landing_url="https://www.academia.edu/72042797/Multiset_ideal_topological_spaces_and_local_functions" data-login_uri="https://www.academia.edu/registrations/google_one_tap" data-moment_callback="onGoogleOneTapEvent" id="g_id_onload"></div><div class="ds-top-related-works--grid-container"><div class="ds-related-content--container ds-top-related-works--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="0" data-entity-id="72042808" 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/72042808/Multiset_ideal_topological_spaces_and_Kuratowski_closure_operator">Multiset ideal topological spaces and Kuratowski closure operator</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="33297539" href="https://independent.academia.edu/BinodTripathy">Binod Tripathy</a></div><p class="ds-related-work--metadata ds2-5-body-xs">SERIES III - 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Similarities and differences between it and the local function are examined by varying several well-known ideals.</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":"Local function versus local closure function in ideal topological spaces","attachmentId":78244276,"attachmentType":"pdf","work_url":"https://www.academia.edu/67421471/Local_function_versus_local_closure_function_in_ideal_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/67421471/Local_function_versus_local_closure_function_in_ideal_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="2" data-entity-id="50812452" 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/50812452/Pre_Local_Function_in_Ideal_Topological_Spaces">Pre-Local Function in Ideal 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="28791139" href="https://mahendra.academia.edu/InternationalJournalofAdvancedScienceandEngineeringIJASE">International Journal of Advanced Science and Engineering (IJASE)</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Int. J. Adv. Sci. Eng., 2021</p><p class="ds-related-work--abstract ds2-5-body-sm">The aim of this paper is to introduce the notation of pre-local function A^(p^* )(I, τ) by using pre-open sets in an ideal topological space (X, τ, I). Some properties and characterizations of a pre-local function are explored Pre-compatible spaces are also defined and investigated. Moreover, by using A^(p^* )(I, τ) we introduce an operator ψ: P(X)→τ satisfying ψ(A) = X-〖(X-A)〗^(p^* )for each A ∈ P(X) and we discuss some characterizations this operator by use pre-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":"Pre-Local Function in Ideal Topological Spaces","attachmentId":68678167,"attachmentType":"pdf","work_url":"https://www.academia.edu/50812452/Pre_Local_Function_in_Ideal_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/50812452/Pre_Local_Function_in_Ideal_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="68741822" 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/68741822/On_some_locally_closed_sets_and_spaces_in_Ideal_Topological_Spaces">On some locally closed sets and spaces in Ideal 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">2015</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper we introduce and characterize some new generalized locally closed sets known as</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 locally closed sets and spaces in Ideal Topological Spaces","attachmentId":79112265,"attachmentType":"pdf","work_url":"https://www.academia.edu/68741822/On_some_locally_closed_sets_and_spaces_in_Ideal_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/68741822/On_some_locally_closed_sets_and_spaces_in_Ideal_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="12121155" 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/12121155/New_Types_of_Multifunctions_in_ideal_Topological_Spaces_via_e_I_Open_sets_and_I_Open_Sets">New Types of Multifunctions in ideal Topological Spaces via e-I-Open sets and -I-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="3632114" href="https://jadara.academia.edu/WadeiFarisAlomeri">Wadei Faris F Alomeri</a></div><p class="ds-related-work--abstract ds2-5-body-sm">The purpose of the present paper is to introduce and investigate two new classes of continuous multifunctions called upper/lower e-I-continuous multifunctions and upper/lower I -continuous multifunctions by using the concepts of e-I-open sets and I -open sets. The class of upper/lower e-I-continuous multifunctions is contained in that of upper/lower I -continuous multifunctions. Several characterizations and fundamental properties concerning upper/lower e-I-continuity and upper/lower I -continuity are 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":"New Types of Multifunctions in ideal Topological Spaces via e-I-Open sets and \u000e\f-I-Open Sets","attachmentId":37432837,"attachmentType":"pdf","work_url":"https://www.academia.edu/12121155/New_Types_of_Multifunctions_in_ideal_Topological_Spaces_via_e_I_Open_sets_and_I_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/12121155/New_Types_of_Multifunctions_in_ideal_Topological_Spaces_via_e_I_Open_sets_and_I_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="5" data-entity-id="117784750" 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/117784750/Applications_of_some_modified_open_sets_in_r_neighbourhood_spaces_with_ideals">Applications of some modified open sets in r-neighbourhood spaces with ideals</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="15587070" href="https://independent.academia.edu/STharmar">S Tharmar</a></div><p class="ds-related-work--metadata ds2-5-body-xs">E3S Web of Conferences</p><p class="ds-related-work--abstract ds2-5-body-sm">The purpose of this paper is to introduce r-a-open sets, r-semi open sets and r-pre open sets in ideal r-neighbourhood space. We also discuss their properties, characterizations and relations with existing notions with suitable examples. Then we develop this paper towards rlimit points and r-interior points in ideal r-neighbourhood space and obtain nice results. 2010 Mathematics Subject Classification. Primary 03E99; Secondary 54A05, 54A10.</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":"Applications of some modified open sets in r-neighbourhood spaces with ideals","attachmentId":113557250,"attachmentType":"pdf","work_url":"https://www.academia.edu/117784750/Applications_of_some_modified_open_sets_in_r_neighbourhood_spaces_with_ideals","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/117784750/Applications_of_some_modified_open_sets_in_r_neighbourhood_spaces_with_ideals"><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="87102703" 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/87102703/Continuity_for_Multifunctions_in_Ideal_Topological_Spaces">Continuity for Multifunctions in Ideal 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="223305291" href="https://independent.academia.edu/Prapartpueon">Prapart pue-on</a></div><p class="ds-related-work--metadata ds2-5-body-xs">WSEAS TRANSACTIONS ON MATHEMATICS, 2021</p><p class="ds-related-work--abstract ds2-5-body-sm">This article presents the concept of ı ⋆ -continuous multifunctions in ideal topological spaces. Especially, several characterizations of ı ⋆ -continuous multifunctions are investigated. Moreover, the relationships between ı ⋆ -continuity and the other types of continuity for multifunctions are established.</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":"Continuity for Multifunctions in Ideal Topological Spaces","attachmentId":91408734,"attachmentType":"pdf","work_url":"https://www.academia.edu/87102703/Continuity_for_Multifunctions_in_Ideal_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/87102703/Continuity_for_Multifunctions_in_Ideal_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="81262818" 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/81262818/Semi_Generalized_Local_Functions_in_Ideal_Generalized_Topological_Spaces">Semi Generalized Local Functions in Ideal Generalized 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="61061816" href="https://independent.academia.edu/DrRehmanJehangir">Dr. Rehman Jehangir</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2011</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper we define semi generalized local function Aµ(I,µ) by using µ-semi-open sets in an ideal generalized topological spaces (X,µ,I). Some properties and characterizations of semi generalized local functions are explored.</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":"Semi Generalized Local Functions in Ideal Generalized Topological Spaces","attachmentId":87368378,"attachmentType":"pdf","work_url":"https://www.academia.edu/81262818/Semi_Generalized_Local_Functions_in_Ideal_Generalized_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/81262818/Semi_Generalized_Local_Functions_in_Ideal_Generalized_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="67421791" 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/67421791/On_preserving_continuity_in_ideal_topological_spaces">On preserving continuity in ideal 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="46679622" href="https://pmf-uns.academia.edu/AleksandarPavlovi%C4%87">Aleksandar Pavlović</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2021</p><p class="ds-related-work--abstract ds2-5-body-sm">We present some sufficient conditions for continuity of the mapping f : 〈X, τ∗ X〉 → 〈Y, τ∗ Y 〉, where τ∗ X and τ ∗ Y are topologies induced by the local function on X and Y , resp. under the assumption that the mapping from 〈X, τX〉 to 〈Y, τY 〉 is continuous. Further, we consider open and closed functions in this matter, as we state the cases in which the open (or closed) mapping is being preserved through the ”idealisation” of both domain and codomain. Through several examples we illustrate that the conditions we considered can not be weakened. AMS Mathematics Subject Classification (2010): 54A10, 54A05, 54B99, 54E99</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 preserving continuity in ideal topological spaces","attachmentId":78244459,"attachmentType":"pdf","work_url":"https://www.academia.edu/67421791/On_preserving_continuity_in_ideal_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/67421791/On_preserving_continuity_in_ideal_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="9" data-entity-id="31411261" 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/31411261/SOME_SUBSETS_OF_IDEAL_TOPOLOGICAL_SPACES">SOME SUBSETS OF IDEAL 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="60044503" href="https://independent.academia.edu/NomanKhalid9">Noman Khalid</a></div><p class="ds-related-work--abstract ds2-5-body-sm">In ideal topological spaces,-dense in itself subsets are used to characterize ideals and mappings. In this note, properties of A I-sets, I-locally closed sets and almost strong I-open sets are discussed. We characterize codense ideals by the collection of these sets. Also, we give a decomposition of continuous mappings and deduce some well-known results.</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 SUBSETS OF IDEAL TOPOLOGICAL SPACES","attachmentId":51778245,"attachmentType":"pdf","work_url":"https://www.academia.edu/31411261/SOME_SUBSETS_OF_IDEAL_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/31411261/SOME_SUBSETS_OF_IDEAL_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":81133880,"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":81133880,"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_81133880" 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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