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.