$ (j-i)sg_\kappa^*$-closed sets and pairwise semi $ t_\omega$-axiom in bispaces

TL;DR

This paper introduces new types of closed sets and semi generalized closed sets in bispaces, and explores their properties and relationships with pairwise semi separation axioms.

Contribution

It defines $(j-i)sg_\kappa^*$-closed sets and studies pairwise semi $T_0$, $T_1$, and $T_\omega$ axioms in bispaces, establishing their interrelations.

Findings

Defined new closed set concepts in bispaces

Analyzed properties of pairwise semi separation axioms

Established relations among these axioms under certain conditions

Abstract

Here we have introduced the ideas of $ (j-i)sg_\kappa^*$-closed sets and a semi generalized closed set in a bispace; $ i,j=1,2; i\not=j $ and then have studied on pairwise semi $T_0 $-axiom, pairwise semi $T_1 $-axiom and pairwise semi $T_\omega $-axiom. We have investigated some of their topological properties and also established a relation among these axioms under some additional conditions.