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Explores the construction and properties of CW complexes, focusing on characteristic maps, closed subsets, products, quotients, and cell formation.
Explores closure finiteness in CW complexes, proving compact subspaces are contained in finite subcomplexes through induction and characteristic maps.
Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.
Demonstrates how to obtain homotopy equivalences between different spaces using the homotopy extension property.
Explores the CW Approximation Theorem, constructing CW complexes from spaces to ensure isomorphism on homology groups.
Covers the construction of a left adjoint to the singular set functor, comparing the homotopy theory of topological spaces with that of simplicial sets.
Delves into applying cellular homology to compute homology groups and Euler characteristic, showcasing its practical implications.
Introduces the Eilenberg-Steenrod axioms in homology theory, defining properties such as homotopy invariance and exactness.
Explores the Fubini Rule for pushouts, emphasizing the importance of transforming diagrams for maintaining pushout properties.
Explores solving the homotopic extension problem, constructing relative CW complexes, and ensuring uniqueness in CW approximations.
Explores the comparison of long exact sequences for vibrations and the relationship between homotopy and homology groups.
