Vietoris–Begle mapping theorem

The Vietoris–Béguin mapping theorem, often simply referred to as the Vietoris theorem, is a result in algebraic topology that pertains to the relationship between homology groups of topological spaces and continuous functions between them. The theorem provides conditions under which the homology of a space can be computed from the homology of a subspace and the mapping properties of a continuous function defined on it.