New separation axioms in generalized bitopological spaces

TL;DR

This paper introduces new separation axioms in generalized bitopological spaces, exploring their properties and relationships with existing axioms, and establishing conditions for their equivalence.

Contribution

It proposes novel separation axioms in generalized bitopological spaces and analyzes their properties and interrelations with known axioms.

Findings

Defined pairwise $T_{1/4}$, $T_{3/8}$, $T_{5/8}$ axioms.

Established mutual relations among separation axioms.

Proved conditions under which these axioms are equivalent.

Abstract

Here we have studied on the ideas of $g_{\mu_i}$ and $\lambda_{\mu_i}$-closed sets with respect to ${\mu_j}(i,j=1,2,i\not=j)$ and pairwise $ \lambda $-closed sets in a generalized bitopological space $ (X,\mu_1, \mu_2) $. We have also investigated the properties on some new separation axioms namely pairwise $ T_\frac{1}{4}$, pairwise $T_\frac{3}{8}$, pairwise $ T_\frac{5}{8} $ and have established their mutual relations with pairwise $ T_0 $, pairwise $ T_\frac{1}{2} $ and pairwise $ T_1 $. We have also shown that under certain conditions these axioms are equivalent.