On regular β^- generalized closed sets in topological spaces

Abstract

In this paper, a new class of sets called regular β^- generalized closed (briefly rβ^g-closed) sets in topological spaces is introduced and properties of this class of sets are studied. A subset of a topological space (X, τ) is called rβ^ -generalized closed (briefly rβ^ g-closed) set if cl(int(cl(A))) ⊆ U whenever A ⊆ U and U is β-open in X. This new class of sets lies between the class of regular closed (briefly r-closed) sets and β^- generalized closed (briefly β^g-closed) sets.