Chapter 2: Basic Topology - Compact Sets

Welcome back to Chapter 2 of Principles of Mathematical Analysis. In this section we study compact sets, which encode a powerful finiteness condition that has far-reaching consequences throughout analysis. Compactness is one of the most important and subtle concepts in the entire book. It generalizes the idea of a closed and bounded subset of the real line to any metric space, and it is the right abstraction for many theorems about continuous functions and convergence.

Slides: https://github.com/petercerno/principles-of-analysis-slides/tree/main/slides/chapter_02_section_03_compact_sets

Видео Chapter 2: Basic Topology - Compact Sets канала Math Meditations