Refining and extending the theoretical foundations of r-near topology

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dc.authorid0000-0002-8134-1004
dc.contributor.authorAydin, Tugce
dc.date.accessioned2026-02-03T11:59:46Z
dc.date.available2026-02-03T11:59:46Z
dc.date.issued2025
dc.departmentÇanakkale Onsekiz Mart Üniversitesi
dc.description.abstractThe present paper aims to refine and extend the theoretical foundations of r-near topology. For this reason, it first redefines the concept of r-near neighborhoods to address inconsistencies in previous studies and clarifies the relationship between r-near open neighborhoods and r-near closure. This study then elaborates on the fundamental properties of r-near closed sets, r-near interior, rnear closure, and r-near neighborhoods. Subsequently, it introduces four novel concepts within rnear topology: r-near accumulation points, r-near isolated points, r-near exterior points, and rnear boundary points. Furthermore, this study explores some of their basic properties and provides illustrative examples regarding the aforesaid concepts. Additionally, it researches the relationships between r-near interior, r-near closure, and r-near exterior in the r-near topological spaces and their classical topological counterparts. Lastly, the study highlights the theoretical significance of r-near topology and suggests potential directions for further research.
dc.identifier.doi10.3934/math.20251335
dc.identifier.endpage30459
dc.identifier.issn2473-6988
dc.identifier.issue12
dc.identifier.scopus2-s2.0-105026261723
dc.identifier.scopusqualityQ1
dc.identifier.startpage30429
dc.identifier.urihttps://doi.org/10.3934/math.20251335
dc.identifier.urihttps://hdl.handle.net/20.500.12428/34412
dc.identifier.volume10
dc.identifier.wosWOS:001651557100001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorAydin, Tugce
dc.language.isoen
dc.publisherAmer Inst Mathematical Sciences-Aims
dc.relation.ispartofAims Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WOS_20260130
dc.subjectnear sets
dc.subjectr-near topology
dc.subjectr-near open sets
dc.subjectr-near accumulation points
dc.subjectr-near boundary points
dc.titleRefining and extending the theoretical foundations of r-near topology
dc.typeArticle

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