THE ABSOLUTELY STRONGLY STAR-HUREWICZ PROPERTY WITH RESPECT TO AN IDEAL

Abstract

A space X is said to have the absolutely strongly star-I-Hurewicz (ASSIH) property if for each sequence (Un : n ∈ N) of open covers of X and each dense subset Y of X, there is a sequence (Fn : n ∈ N) of finite subsets of Y such that for each x ∈ X, {n ∈ N : x ∈/ St(Fn,Un)} ∈ I, where I is the proper admissible ideal of N. In this paper, we investigated the relationship of the ASSIH with related properties and studied the topological properties of the ASSIH. This paper generalizes several results of Song [22, 23] to the larger class of spaces having the ASSIH properties.