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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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5525739 |
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| _version_ | 1832563141890801664 |
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| author | Xiao-Yan Gao Ahmed Mostafa Khalil |
| author_facet | Xiao-Yan Gao Ahmed Mostafa Khalil |
| author_sort | Xiao-Yan Gao |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3b86615b73fe403187f5ed366f704e56 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-3b86615b73fe403187f5ed366f704e562025-02-03T01:20:48ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55257395525739More on Dα-Closed Sets in Topological SpacesXiao-Yan Gao0Ahmed Mostafa Khalil1School of Mathematics and Statistics, Yulin University, Yulin 719000, ChinaDepartment of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, EgyptThe 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.http://dx.doi.org/10.1155/2021/5525739 |
| spellingShingle | Xiao-Yan Gao Ahmed Mostafa Khalil More on Dα-Closed Sets in Topological Spaces Journal of Mathematics |
| title | More on Dα-Closed Sets in Topological Spaces |
| title_full | More on Dα-Closed Sets in Topological Spaces |
| title_fullStr | More on Dα-Closed Sets in Topological Spaces |
| title_full_unstemmed | More on Dα-Closed Sets in Topological Spaces |
| title_short | More on Dα-Closed Sets in Topological Spaces |
| title_sort | more on dα closed sets in topological spaces |
| url | http://dx.doi.org/10.1155/2021/5525739 |
| work_keys_str_mv | AT xiaoyangao moreondaclosedsetsintopologicalspaces AT ahmedmostafakhalil moreondaclosedsetsintopologicalspaces |