CW Complexes: Products and QuotientsExplores the construction and properties of CW complexes, focusing on characteristic maps, closed subsets, products, quotients, and cell formation.
CW Approximation TheoremExplores the CW Approximation Theorem, constructing CW complexes from spaces to ensure isomorphism on homology groups.
Singular homologyIntroduces singular homology, defining singular simplices and explaining the chain complex construction.
Homotopy: DegreeCovers the concept of degree in homotopy theory and the structure of complexes with two simplices.
SimplicesCovers the concept of simplices in delta complexes and explains the standard n-simplex and the ordering of vertices.
Natural Examples of Simplicial SetsIntroduces two fundamental examples of simplicial sets: the nerve of a small category and the singular simplicial set of a topological space.
Closure Finiteness of CW ComplexesExplores closure finiteness in CW complexes, proving compact subspaces are contained in finite subcomplexes through induction and characteristic maps.
