Sets That Exist in A Topological Space and Have the Qualities of Being Ideal and Pre-Semi Open

Abstract

The idea of an ideal topological space, a less robust variation of a topological space, is to be introduced in this essay. The introduction of new kinds of sets by means of the application of a local map is one of the many studies on ideal topological spaces. The paper also investigates various relationships of these sets. The study also concentrates on ideal semi-preopen sets in a topological space. We define pre-semi -interior, pre-semi -closure, and pre-semi -preopen sets and study the fact that most topological properties are unchanged when viewed from an ideal viewpoint. The different kinds of maps in a perfect topological space are also looked into, and their relationships are researched. It is investigated how these ideas relate to other pertinent ideas in ideal topological spaces. The introduction and detailed analysis of the fundamental properties of continuous maps in an ideal topological space