Yayın:
Topologically indistinguishable relations and separation axioms

Basit Görünüm
dc.contributor.authorSibel Demiralp
dc.contributor.authorTareq M. Al-shami
dc.contributor.authorFuad A. Abushaheen
dc.contributor.authorAlaa M. Abd El-latif
dc.date.accessioned2026-01-04T19:54:12Z
dc.date.issued2024-01-01
dc.description.abstract<abstract><p>This study focuses on defining separation axioms for sets without an inherent topological structure. By utilizing a mapping to relate such sets to a topological space, we first define a distinguishable relation over the universal set with respect to the neighborhood systems inspired by a topology of the co-domain set and elucidate its basic properties. To facilitate the way of discovering this distinguishable relation, we initiate a color technique for the equivalence classes inspired by a given topology. Also, we provide an algorithm to determine distinguishable members (or objects) under study. Then, we establish a framework for introducing separation properties within these structureless sets and examine their master characterizations. To better understand the obtained results and relationships, we display some illustrative instances.</p></abstract>
dc.description.urihttps://doi.org/10.3934/math.2024758
dc.description.urihttps://dx.doi.org/10.60692/q98bx-teg46
dc.description.urihttps://dx.doi.org/10.60692/kvwpa-0dy33
dc.description.urihttps://doaj.org/article/eaa8d39d6d424278bb824cb2d6e8c39c
dc.identifier.doi10.3934/math.2024758
dc.identifier.endpage15723
dc.identifier.issn2473-6988
dc.identifier.openairedoi_dedup___::a2484784bc7db5f7e9e7f55be45c197a
dc.identifier.orcid0000-0002-3977-587x
dc.identifier.orcid0000-0002-8074-1102
dc.identifier.orcid0000-0003-0179-2831
dc.identifier.scopus2-s2.0-85191751625
dc.identifier.startpage15701
dc.identifier.urihttps://hdl.handle.net/20.500.12597/41445
dc.identifier.volume9
dc.identifier.wos001219715800001
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)
dc.relation.ispartofAIMS Mathematics
dc.rightsOPEN
dc.subjectRough Sets Theory and Applications
dc.subjectSocial Sciences
dc.subjectGeometry
dc.subjectSeparation axiom
dc.subjectManagement Science and Operations Research
dc.subjectDecision Sciences
dc.subjectAutomata Theory
dc.subjectFuzzy Logic and Residuated Lattices
dc.subjectTopological Spaces
dc.subjectQA1-939
dc.subjectFOS: Mathematics
dc.subjectAxiom
dc.subjectequivalence relation
dc.subjectProbabilistic Rough Sets
dc.subjectMathematical economics
dc.subjectStatistics
dc.subjectApplication of Soft Set Theory in Decision Making
dc.subjectAssociation Rules Mining
dc.subjectProbability Theory
dc.subjectComputer science
dc.subjectComputational Theory and Mathematics
dc.subjectCombinatorics
dc.subjectseparation axioms
dc.subjectComputer Science
dc.subjectPhysical Sciences
dc.subjectSeparation (statistics)
dc.subject$ f\mathcal{t} $-topological distinguishability
dc.subjectMathematics
dc.subject.sdg10. No inequality
dc.subject.sdg4. Education
dc.subject.sdg15. Life on land
dc.subject.sdg16. Peace & justice
dc.titleTopologically indistinguishable relations and separation axioms
dc.typeArticle
dspace.entity.typePublication
local.api.response{"authors":[{"fullName":"Sibel Demiralp","name":null,"surname":"Sibel Demiralp","rank":1,"pid":{"id":{"scheme":"orcid_pending","value":"0000-0002-3977-587x"},"provenance":null}},{"fullName":"Tareq M. Al-shami","name":null,"surname":"Tareq M. Al-shami","rank":2,"pid":{"id":{"scheme":"orcid_pending","value":"0000-0002-8074-1102"},"provenance":null}},{"fullName":"Fuad A. Abushaheen","name":null,"surname":"Fuad A. Abushaheen","rank":3,"pid":null},{"fullName":"Alaa M. Abd El-latif","name":null,"surname":"Alaa M. Abd El-latif","rank":4,"pid":{"id":{"scheme":"orcid","value":"0000-0003-0179-2831"},"provenance":null}}],"openAccessColor":"gold","publiclyFunded":false,"type":"publication","language":{"code":"und","label":"Undetermined"},"countries":null,"subjects":[{"subject":{"scheme":"keyword","value":"Rough Sets Theory and Applications"},"provenance":null},{"subject":{"scheme":"keyword","value":"Social Sciences"},"provenance":null},{"subject":{"scheme":"keyword","value":"Geometry"},"provenance":null},{"subject":{"scheme":"FOS","value":"02 engineering and technology"},"provenance":null},{"subject":{"scheme":"keyword","value":"Separation axiom"},"provenance":null},{"subject":{"scheme":"keyword","value":"Management Science and Operations Research"},"provenance":null},{"subject":{"scheme":"FOS","value":"01 natural sciences"},"provenance":null},{"subject":{"scheme":"keyword","value":"Decision Sciences"},"provenance":null},{"subject":{"scheme":"keyword","value":"Automata Theory"},"provenance":null},{"subject":{"scheme":"keyword","value":"Fuzzy Logic and Residuated Lattices"},"provenance":null},{"subject":{"scheme":"keyword","value":"Topological Spaces"},"provenance":null},{"subject":{"scheme":"keyword","value":"QA1-939"},"provenance":null},{"subject":{"scheme":"FOS","value":"0202 electrical engineering, electronic engineering, information engineering"},"provenance":null},{"subject":{"scheme":"keyword","value":"FOS: Mathematics"},"provenance":null},{"subject":{"scheme":"FOS","value":"0101 mathematics"},"provenance":null},{"subject":{"scheme":"SDG","value":"10. No inequality"},"provenance":null},{"subject":{"scheme":"keyword","value":"Axiom"},"provenance":null},{"subject":{"scheme":"keyword","value":"equivalence relation"},"provenance":null},{"subject":{"scheme":"keyword","value":"Probabilistic Rough Sets"},"provenance":null},{"subject":{"scheme":"keyword","value":"Mathematical economics"},"provenance":null},{"subject":{"scheme":"SDG","value":"4. Education"},"provenance":null},{"subject":{"scheme":"keyword","value":"Statistics"},"provenance":null},{"subject":{"scheme":"keyword","value":"Application of Soft Set Theory in Decision Making"},"provenance":null},{"subject":{"scheme":"keyword","value":"Association Rules Mining"},"provenance":null},{"subject":{"scheme":"SDG","value":"15. Life on land"},"provenance":null},{"subject":{"scheme":"keyword","value":"Probability Theory"},"provenance":null},{"subject":{"scheme":"SDG","value":"16. Peace & justice"},"provenance":null},{"subject":{"scheme":"keyword","value":"Computer science"},"provenance":null},{"subject":{"scheme":"keyword","value":"Computational Theory and Mathematics"},"provenance":null},{"subject":{"scheme":"keyword","value":"Combinatorics"},"provenance":null},{"subject":{"scheme":"keyword","value":"separation axioms"},"provenance":null},{"subject":{"scheme":"keyword","value":"Computer Science"},"provenance":null},{"subject":{"scheme":"keyword","value":"Physical Sciences"},"provenance":null},{"subject":{"scheme":"keyword","value":"Separation (statistics)"},"provenance":null},{"subject":{"scheme":"keyword","value":"$ f\\mathcal{t} $-topological distinguishability"},"provenance":null},{"subject":{"scheme":"keyword","value":"Mathematics"},"provenance":null}],"mainTitle":"Topologically indistinguishable relations and separation axioms","subTitle":null,"descriptions":["<jats:p xml:lang=\"fr\">&lt;abstract&gt;&lt;p&gt;This study focuses on defining separation axioms for sets without an inherent topological structure. By utilizing a mapping to relate such sets to a topological space, we first define a distinguishable relation over the universal set with respect to the neighborhood systems inspired by a topology of the co-domain set and elucidate its basic properties. To facilitate the way of discovering this distinguishable relation, we initiate a color technique for the equivalence classes inspired by a given topology. Also, we provide an algorithm to determine distinguishable members (or objects) under study. Then, we establish a framework for introducing separation properties within these structureless sets and examine their master characterizations. To better understand the obtained results and relationships, we display some illustrative instances.&lt;/p&gt;&lt;/abstract&gt;</jats:p>"],"publicationDate":"2024-01-01","publisher":"American Institute of Mathematical Sciences (AIMS)","embargoEndDate":null,"sources":["Crossref","AIMS Mathematics, Vol 9, Iss 6, Pp 15701-15723 (2024)"],"formats":null,"contributors":null,"coverages":null,"bestAccessRight":{"code":"c_abf2","label":"OPEN","scheme":"http://vocabularies.coar-repositories.org/documentation/access_rights/"},"container":{"name":"AIMS Mathematics","issnPrinted":"2473-6988","issnOnline":null,"issnLinking":null,"ep":"15723","iss":null,"sp":"15701","vol":"9","edition":null,"conferencePlace":null,"conferenceDate":null},"documentationUrls":null,"codeRepositoryUrl":null,"programmingLanguage":null,"contactPeople":null,"contactGroups":null,"tools":null,"size":null,"version":null,"geoLocations":null,"id":"doi_dedup___::a2484784bc7db5f7e9e7f55be45c197a","originalIds":["10.3934/math.2024758","50|doiboost____|a2484784bc7db5f7e9e7f55be45c197a","50|datacite____::48c339b8c3ac8f3d75883a00263a3cca","10.60692/q98bx-teg46","50|datacite____::514ea0c9859b09e5a2e5005795577fed","10.60692/kvwpa-0dy33","oai:doaj.org/article:eaa8d39d6d424278bb824cb2d6e8c39c","50|doajarticles::9d0d2f9d7dc6fcd9c2d0fc5ca4d23906"],"pids":[{"scheme":"doi","value":"10.3934/math.2024758"},{"scheme":"doi","value":"10.60692/q98bx-teg46"},{"scheme":"doi","value":"10.60692/kvwpa-0dy33"}],"dateOfCollection":null,"lastUpdateTimeStamp":null,"indicators":{"citationImpact":{"citationCount":1,"influence":2.5900306e-9,"popularity":3.2544214e-9,"impulse":1,"citationClass":"C5","influenceClass":"C5","impulseClass":"C5","popularityClass":"C5"}},"instances":[{"pids":[{"scheme":"doi","value":"10.3934/math.2024758"}],"type":"Article","urls":["https://doi.org/10.3934/math.2024758"],"publicationDate":"2024-01-01","refereed":"peerReviewed"},{"pids":[{"scheme":"doi","value":"10.60692/q98bx-teg46"}],"type":"Other literature type","urls":["https://dx.doi.org/10.60692/q98bx-teg46"],"publicationDate":"2024-01-01","refereed":"nonPeerReviewed"},{"pids":[{"scheme":"doi","value":"10.60692/kvwpa-0dy33"}],"type":"Other literature type","urls":["https://dx.doi.org/10.60692/kvwpa-0dy33"],"publicationDate":"2024-01-01","refereed":"nonPeerReviewed"},{"alternateIdentifiers":[{"scheme":"doi","value":"10.3934/math.2024758"}],"type":"Article","urls":["https://doaj.org/article/eaa8d39d6d424278bb824cb2d6e8c39c"],"publicationDate":"2024-04-01","refereed":"nonPeerReviewed"}],"isGreen":false,"isInDiamondJournal":false}
local.import.sourceOpenAire
local.indexed.atWOS
local.indexed.atScopus

Dosyalar

Koleksiyonlar

Publications