Eilenberg–Steenrod axioms

Summary

The Eilenberg–Steenrod axioms list the properties that a homology theory on pairs of spaces should have. They are functoriality, homotopy invariance, a long exact sequence for each pair, excision, and a dimension axiom fixing the homology of a point. Singular homology satisfies them, and on finite CW pairs any two theories that satisfy them with the same coefficient group agree. Dropping the dimension axiom gives generalized homology and cohomology theories such as K-theory and cobordism.