On some standard constructions in algebraic topology

In the paper to some known standard constructions in algebraic topology connected with the cohomological structure of a continuous mapping the authorʼs standard construction is added. The last one is served to study perfect zero-dimensional mappings and it is proved that in this case all these constructions lead to equivalent resolvents for Abelian group sheaves, thus to the same spectral sequences. The results of the paper intend to study actions of p-adic group action on topological manifolds, the case that motivated the analysis of spectral sequences connecting the cohomology of a space with p-adic group of transformations and the cohomology of the orbit-space. per is presented to the special issue dedicated to the memory of professor Yuri Michailovich Smirnov. It is a pleasure to the author to recall that Yu.M. Smirnov was the supervisor of his dissertation and that one of his first articles (Zarelua and Smirnov, 1963 [25]) was written in collaboration with Yu.M. Smirnov.