Boundary Analysis

This lecture delves into the concept of boundaries in sets, distinguishing between open and closed sets, and defining the boundary as the collection of points that are not well separated from the set or its complement. The instructor explains how the boundary of a set is related to its interior and closure, providing examples to illustrate these concepts. The lecture concludes with a challenging example involving rational numbers and their density in the real numbers, showcasing the intricate relationship between boundaries, interiors, and closures in mathematical spaces.