$\lambda^*$-closed sets and new separation axioms in Alexandroff spaces

Abstract

Here we have studied the ideas of $g^*$-closed sets, $g\wedge_\tau $-sets and $\lambda^*$-closed sets and investigate some of their properties in the spaces of A. D. Alexandroff [1]. We have also studied some separation axioms like $ T_\frac{\omega}{4}, T_\frac{3\omega}{8}, T_\omega $ in Alexandroff spaces and also have introduced a new separation axiom namely $ T_\frac{5\omega}{8} $ axiom in this space.