In this paper, a new kind of sets called Dα-open sets are introduced and studied in a topological space. 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.
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