Abstract :
For two not necessarily commutative topological groups G and K, let denote the space of all continuous homomorphisms from G to K with the compact-open topology. We prove that if G is metrizable and K is compact then is a k-space. As a consequence we obtain that if D is a dense subgroup of G then is homeomorphicto , and if G is separable h-complete, then the natural map is open onto its image.
