$ Ig^*$-closed sets and its certain properties in $ \sigma $-spaces with respect to an ideal

TL;DR

This paper introduces and investigates the properties of $Ig^*$-closed sets in $\sigma$-spaces with respect to an ideal, along with related separation axioms in Alexandroff spaces.

Contribution

It defines $Ig^*$-closed sets and explores their properties and relations with various $Ig^*$-separation axioms in Alexandroff spaces.

Findings

Introduction of $Ig^*$-closed sets and their properties

Development of $Ig^*$-$T_0$, $T_1$, and $T_ au$ axioms

Relations among the new separation axioms

Abstract

Here we have introduced and studied the idea of $ Ig^*$-closed set with respect to an ideal and investigated some of its properties in Alexandroff spaces. We have also introduced $ Ig^*$-$T_0 $ axiom, $ Ig^*$-$T_1$ axiom, $ Ig^*$-$T_\omega $ axiom and explored a relation among them