More on Ideal Rothberger Spaces

Abstract

The aim of this note is to provide an answer to a question posted in a recent paper. In 2018, after introducing the notion of Ideal Rothberger space, author examines some properties of these spaces. Also there has been a comparison of the spaces (X, τ ), and (X, τ^∗) in terms of being (ideal)Rothberger. According to this, it is shown that if (X, τ^∗) is a Rothberger space, then (X, τ ) is also Rothberger. Therefore, naturally it is asked that, if one can find some extra conditions for ideal I, then the opposite also holds. Thus, for which ideal I, an I-Rothberger space (X, τ ) implies an I-Rothberger space (X, τ^∗)? In this work it has been proved that I is a σ-ideal, and τ is compatible with I, which provides the solution.