Theorems in topology | Homology theory

Excision theorem

In algebraic topology, a branch of mathematics, the excision theorem is a theorem about relative homology and one of the Eilenberg–Steenrod axioms. Given a topological space and subspaces and such that is also a subspace of , the theorem says that under certain circumstances, we can cut out (excise) from both spaces such that the relative homologies of the pairs into are isomorphic. This assists in computation of singular homology groups, as sometimes after excising an appropriately chosen subspace we obtain something easier to compute. (Wikipedia).

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Related pages

Interior (topology) | Compact space | Singular homology | Closure (topology) | Mathematics | Mayer–Vietoris sequence | Relative homology | Homotopy excision theorem | Algebraic topology | Eilenberg–Steenrod axioms