on the topology of δe-open sets

The main purpose of this paper is to introduce and investigate a new class of open sets called δe-open sets. for this aim, first we define and study the notion of e-regular open set via e-closure operator. then, we introduce the notion of δe-open set via e-regular open set. several fundamental properties of the notion of δe-open set have been revealed. also, we show that the family of δe-open sets is a topology strictly weaker than τ δ and stronger than τ . in addition, we investigate relationships between the notion of δe-open set and other existing notions in topology such as open sets, regular open sets and δ-open sets. furthermore, we give not only various properties and characterizations but also examples and counterexamples. finally, some properties related to separation axioms are revealed.