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Proceedings of the American Mathematical Society

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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
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?)

  • Richard F. Arens, A topology for spaces of transformations, Ann. of Math. (2) 47 (1946), 480–495. MR 17525, DOI
  • Wojciech Banaszczyk, Additive subgroups of topological vector spaces, Lecture Notes in Mathematics, vol. 1466, Springer-Verlag, Berlin, 1991. MR 1119302
  • Ernst Binz, Continuous convergence on $C(X)$, Springer-Verlag, Berlin-New York, 1975. Lectures Notes in Mathematics, Vol. 469. MR 0461418
  • H. R. Fisher, LimesrĂ€ume, Math. Ann. 137 (1959), 269-303. E. Hewitt and K. A. Ross, Abstract harmonic analysis, Springer, Berlin, 1963. J. Margalef, E. Outerelo, and J. Pinilla, Topologia, Vol. 5, Alhambra, 1982. M. Megrelishvili, private communication, Seventh Prague Toposym, 1991.
  • Sidney A. Morris, Pontryagin duality and the structure of locally compact abelian groups, Cambridge University Press, Cambridge-New York-Melbourne, 1977. London Mathematical Society Lecture Note Series, No. 29. MR 0442141

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