Interior and Closure in Topology

This lecture covers the concepts of interior and closure of a set in a topological space, defining them as the largest open set contained in the set and the smallest closed set containing the set, respectively. Examples and properties of interior and closure are discussed, emphasizing their role in characterizing the structure of a topological space. The lecture also introduces the notion of isolated points and accumulation points, highlighting their significance in understanding the behavior of sets in a topological context. Furthermore, the lecture explores the union and intersection of subsets in a topological space, illustrating how these operations can be used to analyze the properties of sets and their relationships within the space.