A Study on Soft ARS Closed Sets in Soft Topological Spaces

Abstract

In this work, analogous to Molodtsov Soft sets, We define a new class of Soft sets, namely Soft ARS closed sets and its complement Soft ARS open sets. Further we compare the properties of Soft ARS closed sets with Soft closed set, Soft semi closed set, Soft \(\alpha\) closed set, Soft JP closed set, Soft gsp closed set and we prove the concept of Soft ARS Closed sets is independent of the concept of Soft \(\omega\) closed sets, Soft \(\alpha\)g closed set, Soft gs closed set, Soft gp closed set, Soft pre closed set, Soft Strongly g closed set, Soft g closed, Soft \(\beta\) closed set.We show that the concept of Soft ARS closed sets is stronger than Soft semi closed set and weaker than the concept of Soft generalized semi pre closed sets. The same is applicable for Soft ARS open sets as well. We find the characterization of Soft ARS closed sets and Soft ARS open sets. We investigate fundamental properties of Soft ARS closed sets discuss their properties.