International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1980 / Article

Open Access

Volume 3 |Article ID 713749 | https://doi.org/10.1155/S0161171280000373

J. S. Yang, "On certain groups of functions", International Journal of Mathematics and Mathematical Sciences, vol. 3, Article ID 713749, 14 pages, 1980. https://doi.org/10.1155/S0161171280000373

On certain groups of functions

Received18 Oct 1979

Abstract

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).

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.


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