Spherical Fibrations and Manifolds.
We show that one can reduce the study of global (in particular cohomological) properties of a compact Hausdorff space X to the study of its stable cohomotopy groups . Any cohomology functor on the homotopy category of compact spaces factorizes via the stable shape category ShStab. This is the main reason why the language and technique of stable shape theory can be used to describe and analyze the global structure of compact spaces. For a given Hausdorff compact space X, there exists a metric compact...
We present a very short way of calculating additively the stable (co)homology of Eilenberg-MacLane spaces K(ℤ/p,n). Our method depends only on homological algebra in appropriate categories of functors.