New Classes of Ideal Topological Quotient Maps

Abstract

This abstract introduces the exploration of new classes of ideal topological quotient maps within the field of topology. Topological quotient maps are pivotal in algebraic topology, where a surjective continuous map identifies equivalence relations between points in a space, leading to the creation of a quotient space. This study delves into the development of novel classes of ideal topological quotient maps, contributing to the advancement of theoretical frameworks in algebraic topology. While established classes such as closed, open, proper, and perfect quotient maps provide foundational insights, the pursuit of new classifications aims to enrich our understanding of the intricate relationships between spaces. The abstract underscores the significance of these novelclasses, potentially introducing refined properties or conditions that enhance the applicability of topological quotient maps in diverse mathematical contexts. As the abstract encapsulates the essence of this research, it invites mathematicians and researchers to explore, analyse, and potentially apply these emerging classes in their work, fostering ongoing developments in the field of topology. The purpose of this paper is to study the concept of quotient maps in ideal topological spaces and study some of its stronger forms.