This lecture introduces the Eilenberg-Steenrod axioms in homology theory, which define properties such as homotopy invariance, excision, exactness, and dimension. These axioms uniquely characterize the singular homology on CW complexes.
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Homology is one of the most important tools to study topological spaces and it plays an important role in many fields of mathematics. The aim of this course is to introduce this notion, understand its
Demonstrates the equivalence between simplicial and singular homology, proving isomorphisms for finite s-complexes and discussing long exact sequences.
