Metrizability of locally compact vector spaces
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- by Seth Warner PDF
- Proc. Amer. Math. Soc. 27 (1971), 511-513 Request permission
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
- Robert Ellis, Locally compact transformation groups, Duke Math. J. 24 (1957), 119–125. MR 88674
- 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
- Seth Warner, Compact and finite-dimensional locally compact vector spaces, Illinois J. Math. 13 (1969), 383–393. MR 241946
- Seth Warner, Locally compact commutative artinian rings, Illinois J. Math. 16 (1972), 102–115. MR 293404
Additional Information
- © Copyright 1971 American Mathematical Society
- 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