More on D α -Closed Sets in Topological Spaces

Abstract

The aim of this paper is to present and study topological properties of D α -derived, D α -border, D α -frontier, and D α -exterior of a set based on the concept of D α -open sets. Then, we introduce new separation axioms (i.e., D α − R 0 and D α − R 1 ) by using the notions of D α -open set and D α -closure. The space of D α − R 0 (resp., D α − R 1 ) is strictly between the spaces of α − R 0 (resp., α − R 1 ) and g − R 0 (resp., g − R 1 ). Further, we present the notions of D α -kernel and D α -convergent to a point and discuss the characterizations of interesting properties between D α -closure and D α -kernel. Finally, several properties of weakly D α − R 0 space are investigated.

Retracted: More on Dα-Closed Sets in Topological Spaces

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