Covers homology with coefficients, introducing the concept of defining homology groups with respect to arbitrary abelian groups.
Covers induced homomorphisms, homotopy invariance, and homology groups of quotients.
Delves into the invariance of domain theorem, proving that a subset homeomorphic to an open subset is open itself, with implications for embeddings and homeomorphisms.
Covers the concept of orientation and degrees in topology, focusing on assigning orientations to manifolds.
Explores path lifting, homotopy properties, and homomorphisms in covering spaces.
Explores the construction and properties of CW complexes, focusing on characteristic maps, closed subsets, products, quotients, and cell formation.
Covers the proof of Theorem A, discussing homology, quotients, and isomorphisms.
Covers the proof of the Jordan Curve Theorem and the properties of embedded spheres.
Introduces reduced homology groups and explains their properties and applications in topology.
Covers the concept of simplices in delta complexes and explains the standard n-simplex and the ordering of vertices.
