Аннотация:We present approaches to substitute the acting groups of G-spaces that preserve various properties of actions, such as transitivity, being a coset space, and preserving a fixed equiuniformity in case of a G-Tychonoff space. Such substitutions make it possible to obtain bounds on cardinal invariants of acting groups with admissible topologies, and to investigate metrizability of phase spaces and find their equivariant completions of the same weight.