ON THE UNIVERSAL COEFFICIENT FORMULA AND DERIVED LIMIT FUNCTOR

It is known that homology and inverse limit functors do not commute. In the paper, we consider this very problem and find its application for various homology theories. In particular, on the category of general topological spaces, there are some exact homology functors induced by different non-free cochain complexes. The relation between them and other classical homology theories is given. In addition, for the defined homology functors, the tautness and the continuous properties are obtained.