ON BI-TOPOLOGICAL SPACE

Abstract

Bi-topological spaces, a generalization of traditional topological spaces, provide a rich framework for studying the interplay between two distinct topologies defined on a single set. In a bi-topological space, open sets and neighborhoods are characterized by two separate systems of open sets, offering a nuanced understanding of continuity, convergence, and compactness properties. This abstract explores the foundational concepts of bi-topological spaces, including their definition, basic properties, and key theorems. Moreover, it discusses the significance of bi-topological spaces in various mathematical contexts, highlighting their applications in fields such as functional analysis, differential equations, and computer science. Through the lens of bi-topological spaces, these abstract illuminates the versatility and relevance of this mathematical structure in both theoretical investigations and practical applications.