On some standard constructions in algebraic topology

The paper 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.