R-factorizable G-spaces

The concept of an R-factorizable G-space is introduced. It is shown that quotients of R-factorizable groups are R-factorizable G-spaces; that the action of an R-factorizable group G on its quotient space X can be extended to an action of the realcompactification vG of G on the realcompactification vX of X; and that vX is Gδ-closed in the completion of X with respect to the maximal equiuniformity. The spectral representations of R-factorizable G-spaces are presented.