The Mayer-Vietoris Theorem is a fundamental result in algebraic topology that provides a method for computing the homology groups of a topological space by breaking it down into simpler pieces. It involves taking two open sets whose union covers the space, calculating their individual homologies, and using information from their intersection to derive the overall homology. This theorem not only highlights the power of decomposition in topology but also connects closely with concepts like cellular homology and excision.
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