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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

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