Yu.M. Smirnovʼs general equivariant shape theory

A general equivariant shape theory for arbitrary G-spaces in the case of a compact group G is constructed by using the method of pseudometrics suggested by Yu.M. Smirnov as early as in 1985 at the fifth Tiraspol Symposium on General Topology and Its Applications (Smirnov, 1985 [7]).