On homomorphism spaces of metrizable groups

Details On homomorphism spaces of metrizable groups On homomorphism spaces of metrizable groups

2002-08-14

arxiv.org/abs/math/0208115v2

J. Pure Appl. Algebra 182 (2003), no. 2-3, 263--267

Mathematics

General Topology

v3 (revision of March 17, 2003): slight changes in general, the proof of the last theorem has been rewritten

Scientific paper

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.

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