|
Organizers |
On homomorphism spaces of metrizable groups
by
Gábor Lukács
York University
In this talk we will present a generalization of a result by Chasco, who proved that for every abelian metrizable group G, its dual group [^G] (i.e. the group of continuous homomorphisms into the unit circle, T) is a k-space in the compact-open topology.
We prove that the space of continuous homomorphisms H(G, K) in the compact-open topology is a k-space whenever G is a (not necessarily commutative) metrizable topological group and K is a compact topological group which satisfies certain not too restrictive conditions.
As a consequence we obtain that if D is a dense subgroup of G then H(D, K) is homeomorphic to H(G, K), and if G is separable h-complete, then the natural map G --> C(H(G, K), K) is open onto its image.
Date received: March 13, 2003
Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cajv-09.