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On certain groups of functions

J. S. Yang

International Journal of Mathematics and Mathematical Sciences, 1980, vol. 3, 1-14

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 M p = { f ∈ C ( 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 ) .

Date: 1980
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:713749

DOI: 10.1155/S0161171280000373

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