On the topology of $\delta_e$-open sets

Journal of Linear and Topological Algebra

دوره 12، شماره 02، شهریور 2023، صفحه 119-131   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.30495/jlta.2023.703518

نویسندگان

C. ‎Dalk{\i}ran¹؛ M. ‎\"{O}zko\c{c}^{* 2}

¹M\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

²M\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

چکیده

‎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.

کلیدواژه‌ها

$\delta_e$-open؛ $\delta_e$-continuity؛ $\delta_e$-Hausdorff space؛ $\delta_e$-regular space؛ $\delta_e$-normal space

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