A reflexive admissible topological group must be locally compact
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- by Elena Martín Peinador PDF
- Proc. Amer. Math. Soc. 123 (1995), 3563-3566 Request permission
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
- Richard F. Arens, A topology for spaces of transformations, Ann. of Math. (2) 47 (1946), 480–495. MR 17525, DOI 10.2307/1969087
- Wojciech Banaszczyk, Additive subgroups of topological vector spaces, Lecture Notes in Mathematics, vol. 1466, Springer-Verlag, Berlin, 1991. MR 1119302, DOI 10.1007/BFb0089147
- Ernst Binz, Continuous convergence on $C(X)$, Lecture Notes in Mathematics, Vol. 469, Springer-Verlag, Berlin-New York, 1975. MR 0461418, DOI 10.1007/BFb0088826 H. R. Fisher, Limesräume, 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, London Mathematical Society Lecture Note Series, No. 29, Cambridge University Press, Cambridge-New York-Melbourne, 1977. MR 0442141, DOI 10.1017/CBO9780511600722
Additional Information
- © Copyright 1995 American Mathematical Society
- 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