The main purpose of this paper is to introduce and investigate a new class of open sets called $\delta_e$-open sets. For this aim, first we define and study the notion of $e$-regular open set via $e$-closure operator. Then, we int
أکثر
The main purpose of this paper is to introduce and investigate a new class of open sets called $\delta_e$-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 $\delta_e$-open set via $e$-regular open set. Several fundamental properties of the notion of $\delta_e$-open set have been revealed. Also, we show that the family of $\delta_e$-open sets is a topology strictly weaker than $\tau^{\delta}$ and stronger than $\tau$. In addition, we investigate relationships between the notion of $\delta_e$-open set and other existing notions in topology such as open sets, regular open sets and $\delta$-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.
تفاصيل المقالة