Extension of G-uniform maps

The notion of a G-uniform function was introduced by Jan de Vies in order to prove that, if G is a locally compact Hausdorff group, then any completely regular G-space admits a G-compactification. In this paper, for a locally compact Hausdorff group G, we establish analogs of the well known Urysohn Lemma and Tietze Extension Theorem for G-uniform functions. We examine also the extension problem for vector-valued G-uniform maps.