Continuity of Mapping: Understanding Paths and Centers

This lecture discusses the concept of continuity of a mapping, focusing on the relationship between open sets and the continuity of functions. It covers the idea of paths between points, the center of openings, and the properties of mappings. The instructor explains how to show the continuity of a mapping by considering the containment of points in open sets. Additionally, the lecture explores the connection between paths and functions, emphasizing the importance of understanding the relationship between different elements in mathematical spaces.