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A reflexive admissible topological group must be locally compact


Author: Elena MartĂ­n Peinador
Journal: Proc. Amer. Math. Soc. 123 (1995), 3563-3566
MSC: Primary 22B05; Secondary 54H11
DOI: https://doi.org/10.1090/S0002-9939-1995-1301516-4
MathSciNet review: 1301516
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Abstract: Let G be a reflexive topological group, and $G\hat \emptyset$ its group of characters, endowed with the compact open topology. We prove that the evaluation mapping from $G\hat \emptyset \times G$ into the torus T is continuous if and only if G is locally compact. This is an analogue of a well-known theorem of Arens on admissible topologies on $C(X)$.


References [Enhancements On Off] (What's this?)

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Keywords: Admissible topology, compact open topology, reflexive group, continuous convergence structure, locally compact
Article copyright: © Copyright 1995 American Mathematical Society