ИСТИНА

The concept of R-factorizable G-space is introduced. The quotients of R-factorizable groups are R-factorizable G-spaces and in this case they are characterized in the similar way as R-factorizable groups. Moreover, R-factorizablility characterize those compact coset spaces which are coset spaces of w-narrow groups. It is shown that the action of R-factorizable group G on its quotient space X is extended to the action on their realcompactifications vG and vX and that vX is G_\delta-closed in the completion of X with respect to the maximal equiuniformity.