Extending uniformly continuous pseudo-ultrametrics and uniform retracts

Ellis, Robert L.

doi:10.1090/S0002-9939-1971-0283752-5

Extending uniformly continuous pseudo-ultrametrics and uniform retracts
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Proc. Amer. Math. Soc. 30 (1971), 599-602 Request permission

Abstract:

It is first proved that any uniformly continuous pseudo-ultrametric on a subspace of a non-Archimedean uniform space X has a uniformly continuous extension to X (which preserves total boundedness or separability). Then it is proved that every complete subspace of an ultrametrizable space X is a uniform retract of X. This has consequences concerning the extension of uniformly continuous functions.

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