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On the Extension of Uniformly Continuous Functions(1)

Published online by Cambridge University Press:  20 November 2018

L. T. Gardner  and
P. Milnes
L. T. Gardner
Affiliation:
Department of Mathematics, University of Toronto Toronto, Canada M5S 1A1
P. Milnes
Affiliation:
Department of Mathematics, University of Western Ontario Toronto, Ontario N6A 3K7
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Abstract

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A theorem of M. Katětov asserts that a bounded uniformly continuous function f on a subspace Q of a uniform space P has a bounded uniformly continuous extension to all of P. In this note we give new proofs of two special cases of this theorem: (i) Q is totally bounded, and (ii) P is a locally compact group and Q is a subgroup, both P and Q having the left uniformity.

Keywords

Primary 46J1054E15Secondary 43A15Uniform spaceuniformly continuous functionextensionlocally compact group
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 1 , April 1975 , pp. 143 - 145
Copyright
Copyright © Canadian Mathematical Society 1975

Footnotes

(1)

This research was supported in part by NRC grants A4006 and A7857.

References

1. Dixmier, J., Les C*-algébres et leurs représentations, Gauthier-Villars, Paris, 1964.Google Scholar
2. Gantner, T. E., Some corollaries to the metrization lemma, Amer. Math. Monthly 76 (1969), 45-47.Google Scholar
3. Hewitt, E. and Ross, K. A., Abstract Harmonic Analysis I, Springer-Verlag, Berlin, 1963.Google Scholar
4. Katětov, M., On real-valued functions in topological spaces, Fund. Math. 38 (1951), 85–91, and correction, Fund. Math. 40 (1953), 203-205.Google Scholar
5. Kelley, J. L., General Topology, D. Van Nostrand, Princeton, 1955.Google Scholar
6. Milnes, P., Compactifications of semitopological semigroups (to appear in J. Australian Math. Soc).Google Scholar
7. Simmons, G. F., Introduction to topology and modern analysis, McGraw-Hill, New York, 1963.Google Scholar
8. Weil, A., Sur les espaces à structure uniforme et sur la topologie générale, Hermann, Paris, 1937.Google Scholar