Some Separation Axioms in Topological Spaces

TL;DR

This paper introduces new separation axioms in topology based on specific open sets, expanding the classification of topological spaces and exploring their properties.

Contribution

The paper defines novel $ SC^* $ and $ H^* $-separation axioms using specialized open sets, enriching the framework of separation axioms in topology.

Findings

Defined new $ SC^* $-separation axioms including $ C_0 $ and $ C_1 $ variants.

Defined $ H^* $-separation axioms such as $ T_{1/2} $, $ T_b $, and $ T_d $.

Established properties and relationships of spaces satisfying these axioms.

Abstract

In this paper, we introduced the concepts of new separation axioms called $ SC^* $-separation axioms and $ H^* $-separation axioms by using $ SC^* $ and $ H^* $-open sets in topological spaces. The $ SC^* $-separation axioms include $ SC^* $-$ C_0 $, $ SC^* $-$ C_1 $, weakly $ SC^* $-$ C_0 $, and weakly $ SC^* $-$ C_1 $ spaces, while the $ H^* $-separation axioms include $ H^* $-$ T_{\frac{1}{2}} $, $ H^* $-$ T_b $, and $ H^* $-$ T_d $ spaces. Also, we obtained several properties of such spaces.