New separation axioms in generalized bitopological spaces

Abstract

Here we have studied on the ideas of $g_{μ_i}$ and $λ_{μ_i}$-closed sets with respect to ${μ_j}(i,j=1,2,i\not=j)$ and pairwise $ λ$-closed sets in a generalized bitopological space $ (X,μ_1, μ_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.