The Homology of Product Spaces

Abstract

If two or more spaces are related to each other in some way, we would naturally expect that their homology groups should also be related in some way. Some of the most important theorems in the preceding chapters bear out this expectation : If A is a subspace of X, the exact homology sequence of the pair (X,A) describes the relations between the homology groups of A and the homology groups of X. If the space X is the union of two subspaces U and V, then the Mayer—Vietoris sequence gives relations between the homology groups of U, V, U∩V, and X.