A Study on Topological Space for an Ideal Topological Space

Abstract

An ideal topological space is a triplet (X, τ, ℑ), where X is a nonempty set, τ is a topology on X, and ℑ is an ideal of subsets of X. In this paper, we introduce L^∗-perfect, R^∗-perfect, and C^∗-perfect sets in ideal spaces and study their properties. We obtained a characterization for compatible ideals via R^∗-perfect sets. Also, we obtain a generalized topology via ideals which is finer than τ using R^∗-perfect sets on a finite set.