Strong excision and strong shape invariance are equivalent for homology theories on the category of compact metric pairs

In 1960, Milnor gave an axiomatic characterization of Steenrod homology as an ordinary homology theory on the category of compact metric pairs satisfying the strong excision axiom and the cluster axiom. The subject of this paper is to explore the role of the strong excision axiom on its own. It is proved that for any homology theory on the category of compact metric pairs strong excision is equivalent to strong shape invariance.

Keywords

strong shape theory, homology theory, strong excision axiom

2010 Mathematics Subject Classification

55N20, 55N40, 55P55

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Published 1 January 2008