Closure Finiteness of CW Complexes

This lecture discusses the closure finiteness property of CW complexes, proving that a compact subspace of a complex X is contained in a finite subcomplex. The proof involves showing that the compact subspace meets only finitely many cells, leading to the conclusion that the space is closed. The lecture further explores the process of induction and characteristic maps to demonstrate the closure finiteness property. It concludes by illustrating how a single cell can be contained in a finite subcomplex, emphasizing the finite nature of the subcomplexes within the complex.