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Proceedings of the American Mathematical Society

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Metrizability of locally compact vector spaces


Author: Seth Warner
Journal: Proc. Amer. Math. Soc. 27 (1971), 511-513
MSC: Primary 46.01
DOI: https://doi.org/10.1090/S0002-9939-1971-0270114-X
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 19, 561. MR 0088674 (19:561b)
  • [2] Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis, Vol. I: Structure of topological groups. Integration theory, group representations, Die Grundlehren der math. Wissenschaften, Band 115, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #158. MR 551496 (81k:43001)
  • [3] Seth Warner, Compact and finite-dimensional locally compact vector spaces, Illinois J. Math. 13 (1969), 383-393. MR 39 #3282. MR 0241946 (39:3282)
  • [4] -, Locally compact commutative artinian rings, Illinois J. Math. (to appear). MR 0293404 (45:2481)

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Additional Information

DOI: https://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

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