More on Dα-Closed Sets in Topological Spaces

• Main Authors: Xiao-Yan Gao, Ahmed Mostafa Khalil
• Format: Article
• Language: English
• Published: Hindawi Limited 2021-01-01
• Series: Journal of Mathematics
• Online Access: http://dx.doi.org/10.1155/2021/5525739

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.