STEENROD-ČECH HOMOLOGY-COHOMOLOGY THEORIES ASSOCIATED WITH BIVARIANT FUNCTORS

Let NG₀ denote the category of all pointed numerically generated spaces and continuous maps preserving base-points. In [SYH], we described a passage from bivariant functors NG₀^op × NG₀ → NG₀ to generalized homology and cohomology theories. In this paper, we construct a bivariant functor such that the associated cohomology is the Čech cohomology and the homology is the Steenrod homology (at least for compact metric spaces).