This paper explores the concept of intuitionistic topological spaces, delving into their definitions and essential properties. It also examines intuitionistic topological subspaces, providing insights into their characteristics. Additionally, the paper investigates intuitionistic regular spaces and demonstrates their hereditary nature, specifically focusing on Β and . To illustrate these concepts in practical terms, the paper presents two real-world examples of intuitionistic sets. Through a comprehensive analysis of intuitionistic topological spaces and their subsets, the study sheds light on the inheritability of regularity in these spaces. Furthermore, the work emphasizes the significance of intuitionistic topological spaces within the realm of mathematical research, showcasing their applicability through concrete instances of intuitionistic sets
