  For 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.
