- (X, A)
If one has defined a homology theory over compact pairs, it is possible to extend it into a compactly supported homology theory in the wider category of Hausdorff pairs (X, A) with A closed in X, by defining that the homology of a Hausdorff pair (X, A) is the direct limit over pairs (Y, B), where Y, B are compact, Y is a subset of X, and B is a subset of A.
- Kreck, Matthias (2010), Differential Algebraic Topology: From Stratifolds to Exotic Spheres, Graduate Studies in Mathematics, 110, American Mathematical Society, p. 95, ISBN 9780821848982.
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