An important consequence of a result of Katětov and Morita states that every metrizable space is contained in a complete metrizable space of the same dimension. We give an equivariant version of this fact in the case of a locally compact $\sigma$-compact acting group.
@article{118694, author = {Michael Megrelishvili}, title = {Equivariant completions}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {35}, year = {1994}, pages = {539-547}, zbl = {0871.54040}, mrnumber = {1307281}, language = {en}, url = {http://dml.mathdoc.fr/item/118694} }
Megrelishvili, Michael. Equivariant completions. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) pp. 539-547. http://gdmltest.u-ga.fr/item/118694/
General Topology, Parts 1, 2, Hermann Paris (1966). (1966)
Topologie Générale, Ch. IX,X, Hermann Paris (1958). (1958) | MR 0173226
Extensions of Minimal Transformation Groups, Sijthoff & Noordhoff, Alphen aan den Rijn, 1979. | MR 0550605
A construction of the greatest ambit, Math. Systems Theory 4 (1970), 243-248. (1970) | MR 0267038
Topological Groups: Characters, Dualities and Minimal Group Topologies, Marcel Dekker: Pure Appl. Math. 130 (1989). (1989) | MR 1015288
General Topology, P.W.N., Warszawa (1977). (1977) | MR 0500780 | Zbl 0373.54002
The action of a locally compact group on a metric space, Nieuw Arch. Wisk. (3) 7 (1959), 70-74. (1959) | MR 0124434 | Zbl 0092.02802
Extension of mappings on metric spaces, Fund. Math. 68 (1960), 251-263. (1960) | MR 0124026 | Zbl 0100.18903
Uniform Spaces, AMS, Providence, Rhode Island (1964). (1964) | MR 0170323 | Zbl 0124.15601
On the dimension of non-separable spaces I, Czech. Math. J. 2 (1952), 333-368. (1952) | MR 0061372
Quasibounded uniform $G$-spaces (in Russian), Manuscript deposited at Gruz. NIINTI (Tbilisi) on March 3, 1987, No.331-G.
A Tychonoff $G$-space not admitting a compact Hausdorff $G$-extension or $G$-linearization, Russ. Math. Surv. 43:2 (1988), 177-178. (1988) | MR 0940673
Compactification and factorization in the category of $G$-spaces, Categorical Topology and its Relation to Analysis, Algebra and Combinatorics J. Adámek, S. MacLane World Scientific Singapore (1989), 220-237. (1989) | MR 1047903
Normal families and dimension theory in metric spaces, Math. Ann. 128, N4 (1954), 143-156. (1954) | MR 0065906
Automorphisms of locally compact groups, Pacific J. Math. 76 (1978), 143-146. (1978) | MR 0578732 | Zbl 0354.22010
Universal topological transformation groups, General Topology and its Applications 5 (1975), 107-122. (1975) | MR 0372834 | Zbl 0299.54030
Topological Transformation Groups I: A Categorical Approach, Math. Centre Tract 65 Mathematisch Centrum, Amsterdam (1975). (1975) | MR 0415586
On the existence of $G$-compactifications, Bull. Ac. Polon. Sci. Ser. Math. 26 (1978), 275-280. (1978) | MR 0644661 | Zbl 0378.54028