A factor of singular homology
Singular homology is a beautiful theory, in which we can see a clear correspondence between Algebra and Topology. However, it behaves badly on topological spaces which are not locally simply connected in comparison with Čech homology. In the present paper we introduce a canonical factor \(H^ T_ n(X)\) of singular homology \(H_ n(X)\), which agrees with singular homology on ANR's and behaves well on the indicated spaces. We also introduce a notion of ``quasi-homotopy'' for continuous maps. It turns out that the factor is invariant under quasi-homotopy.
scientific article; zbMATH DE number 61122