Article contents
On the Extension of Uniformly Continuous Functions(1)
Published online by Cambridge University Press: 20 November 2018
Abstract
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
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1975
Footnotes
This research was supported in part by NRC grants A4006 and A7857.
References
- 1
- Cited by