On the Steenrod homology theory of compact spaces (Q1191396)

A new axiomatic characterization of the Steenrod homology on the category of all compact Hausdorff spaces is given. It is formulated in terms of bifunctor homology theory (homology group depends on both: space and coefficients) and is based on Eilenberg-Steenrod axioms. The characterization is very relevant to Eilenberg-Steenrod theorem on uniqueness of the Čech cohomology theory defined on all compact spaces. As a consequence author obtains the following proposition: A homology theory on the category of compact Hausdorff spaces is isomorphic to the Steenrod homology theory if and only if it is an exact theory which is isomorphic to the Čech theory for every infinitely divisible abelian group.