A note on extensions of open sets by idealizations

Abstract

Recently, Abbas [1] has introduced and investigated the notion of h-open sets in a topological space. As a generalization of h-open sets, in [2] we introduced hIopen sets in an ideal topological space (X, τ, I) and obtained some properties of hI-open sets. In this paper, we introduce and investigate h ⋆ -open sets on an ideal topological space. We show that h ⋆ -open sets lie between open sets and hI-open sets and h ⋆ -open sets are indepenent of h-open sets.