**I. Bakhia**

## On the Dimension Modulo Classes of Topological Spaces
and Free Topological Groups

**abstract:**

Functions of dimension modulo a (rather wide) class of spaces are considered and
the conditions are found, under which the dimension of the product of spaces
modulo these classes is equal to zero. Based on these results, the sufficient
conditions are established, under which spaces of free topological semigroups
(in the sense of Marxen) and spaces of free topological groups (in the sense of
Markov and Graev) are zero-dimensional modulo classes of compact spaces.