Some applications of Dα-closed sets in topological spaces

•We propose a new kind of sets called Dα-closed, Dα-open, Dα-continuous and Dα-open function.•We introduce the notion of Dα-closed graph and strongly Dα-closed graph by using Dα-closed set.•We introduce the notion of Dα-T1 and Dα-T2 by using Dα-open set.

In this paper, a new kind of sets called Dα-open sets are introduced and studied in a topological spaces. The class of all Dα-open sets is strictly between the class of all α-open sets and g-open sets. Also, as applications we introduce and study Dα-continuous, Dα-open, and Dα-closed functions between topological spaces. Finally, some properties of Dα-closed and strongly Dα-closed graphs are investigated.