On the topology of $\delta_e$-open sets
Subject Areas : General topology
C. ‎Dalk{\i}ran
1
,
M. ‎\"{O}zko\c{c}
2
1 - M\u{g}ula S{\i}tk{\i} Ko\c{c}man University, Graduate School of Natural and Applied Sciences, Mathematics, 48000, Mente\c{s}e-Mu\u{g}la, Turkey
2 - M\u{g}ula S{\i}tk{\i} Ko\c{c}man University, Faculty of Science, Department of Mathematics, 48000, Mente\c{s}e-Mu\u{g}la, Turkey
Keywords: $\delta_e$-open, $\delta_e$-continuity, $\delta_e$-Hausdorff space, $\delta_e$-regular space, $\delta_e$-normal space,
Abstract :
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.
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