Elementary Algebraic Topology
The Excision Theorem is a fundamental result in algebraic topology that allows for the simplification of homology computations by stating that if a space is replaced by a subspace that is 'nice enough,' the homology groups remain unchanged. This theorem plays a crucial role in understanding how homology behaves under the removal of certain subsets and helps in computations involving singular simplices and chains, as well as in establishing relationships within the Mayer-Vietoris sequence.
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