New separation axioms in generalized bitopological spaces

Abstract

Here we have studied on the ideas of $g_{{\mu }_i}$ and ${\lambda }_{{\mu }_i}$-closed sets with respect to ${\mu }_j(i,j=1,2,i\ne j)$ 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.

13 pages