$beta^*$g−closed sets and new separation axioms

Abstract

In this paper, by using $beta^*$−set [24] we introduce a new class of sets called $beta^*$ g−closed sets, which is stronger than g−closed sets and weaker than closed sets. We define two new separation axioms called $beta^* T_{1/2}$ and $beta^{**}T_{1/2}$ spaces as applications of $beta^*$ g−closed sets. The notions $beta^*$ g−continuity and $beta^*$g−irresoluteness are also introduced. 2000 Mathematics Subject Classifications: 54C08, 54A05