Equivariant embeddings and ?-bounded groups
Por:
Antonyan S.A.
Publicada:
1 ene 1994
Resumen:
A topological group is called the ?-bounded one if it is covered by an account number of shifts of any neighbourhood of its unit. It is proved that the ?-boundedness of a group G is equivalent to that circumstance that in the space C(G) of all continuous mappings f:G?[0, 1] in the compactly open topology any uniformly continuous compact is metrizable. By means of the criterion it is established that if G is ?-bounded group then any G-Tichonov space admits equivariant embedding in the multiplication with the same weight of metrizable convex compact subspaces of a space C(G). The subspaces have affine actions of group G.