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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Metrizability of locally compact vector spaces


Author: Seth Warner
Journal: Proc. Amer. Math. Soc. 27 (1971), 511-513
MSC: Primary 46.01
MathSciNet review: 0270114
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Abstract: By use of the theory of characters and the Pontryagin-van Kampen theorem, it is shown that if $ E$ is a locally compact vector space over a discrete division ring $ K$ of characteristic zero and if $ {\dim _K}E < {2^\mathfrak{m}}$, where $ \mathfrak{m}$ is the cardinality of $ K$, then $ E$ is metrizable.


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

  • [1] Robert Ellis, Locally compact transformation groups, Duke Math. J. 24 (1957), 119–125. MR 0088674
  • [2] Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496
  • [3] Seth Warner, Compact and finite-dimensional locally compact vector spaces, Illinois J. Math. 13 (1969), 383–393. MR 0241946
  • [4] Seth Warner, Locally compact commutative artinian rings, Illinois J. Math. 16 (1972), 102–115. MR 0293404

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0270114-X
Keywords: Topological vector space, topological algebra, locally compact, metrizability
Article copyright: © Copyright 1971 American Mathematical Society