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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 Hindawi Publishing Corporation. 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 C(X,G) denote the group of continuous functions from a topological space X into a topological group G with the pointwise multiplication and the compact-open topology. We show that there is a natural topology on the collection of normal subgroups Δ(X) of C(X,G) of the Mp={fC(X,G):f(p)=e} which is analogous to the hull-kernel topology on the commutative Banach algegra C(X) of all continuous real or complex-valued functions on X. We also investigate homomorphisms between groups C(X,G) and C(Y,G).