International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 3, Pages 491-504
On certain groups of functions
Department of Mathematics, Computer Science, and Statistics, University of South Carolina, Columbia 29208, South Carolina, USA
Received 18 October 1979
Copyright © 1980 J. S. Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let denote the group of continuous functions from a topological space into a topological group with the pointwise multiplication and the compact-open topology. We show that there is a natural topology on the collection of normal subgroups of of the which is analogous to the hull-kernel topology on the commutative Banach algegra of all continuous real or complex-valued functions on . We also investigate homomorphisms between groups and .