More on Dα-Closed Sets in Topological Spaces

The aim of this paper is to present and study topological properties of Dα-derived, Dα-border, Dα-frontier, and Dα-exterior of a set based on the concept of Dα-open sets. Then, we introduce new separation axioms (i.e., Dα−R0 and Dα−R1) by using the notions of Dα-open set and Dα-closure. The space of...

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Bibliographic Details
Published inJournal of mathematics (Hidawi) Vol. 2021; pp. 1 - 9
Main Authors Gao, Xiao-Yan, Khalil, Ahmed Mostafa
Format Journal Article
LanguageEnglish
Published Cairo Hindawi 2021
Hindawi Limited
Subjects
Axioms
Cognition & reasoning
Kernels
Mathematics
Topology
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Summary:The aim of this paper is to present and study topological properties of Dα-derived, Dα-border, Dα-frontier, and Dα-exterior of a set based on the concept of Dα-open sets. Then, we introduce new separation axioms (i.e., Dα−R0 and Dα−R1) by using the notions of Dα-open set and Dα-closure. The space of Dα−R0 (resp., Dα−R1) is strictly between the spaces of α−R0 (resp., α−R1) and g−R0 (resp., g−R1). Further, we present the notions of Dα-kernel and Dα-convergent to a point and discuss the characterizations of interesting properties between Dα-closure and Dα-kernel. Finally, several properties of weakly Dα−R0 space are investigated.
ISSN:2314-4629
2314-4785
DOI:10.1155/2021/5525739