2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64725For two not necessarily commutative topological groups G and T, let H(G,T) denote the space of all continuous homomorphisms from G to T with the compact-open topology. We prove that if G is metrizable and T is compact then H(G,T) is a k-space. As a consequence we obtain that if G_1 is a dense subgroup of G then H(G_1,T) is homeomorphic to H(G,T), and if G is separable h-complete, then the natural map G --> C(H(G,T),T) is open onto its image.v3 (revision of March 17, 2003): slight changes in general, the proof of the last theorem has been rewrittenGeneral TopologyGroup Theory22A05text