Chapter 2: Basic Topology - Perfect Sets

Welcome back to Chapter 2 of Principles of Mathematical Analysis. In this section we study perfect sets. A perfect set is a closed set in which every point is a limit point, so there are no isolated points. These look like small, rigid objects, but we will see that they are always very large in a specific sense: every nonempty perfect set in Euclidean space is uncountable. As a striking application we will build the Cantor set, a perfect subset of the unit interval that contains no segment at all, yet is still uncountable. It is one of the most famous examples in analysis and in topology.

Slides: https://github.com/petercerno/principles-of-analysis-slides/tree/main/slides/chapter_02_section_04_perfect_sets

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