On the Universal Coefficient Formula and Derived $\varprojlim ^{(i)} $ Functor

Abstract: 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 defined exact homology functors induced by different non-free cochain complexes. Relation between them and other classical homology theories are given. In addition, for the defined homology functors the tautness and the continuous properties are obtained.