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Proceedings of the American Mathematical Society

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Extending uniformly continuous pseudo-ultrametrics and uniform retracts


Author: Robert L. Ellis
Journal: Proc. Amer. Math. Soc. 30 (1971), 599-602
MSC: Primary 54.30
DOI: https://doi.org/10.1090/S0002-9939-1971-0283752-5
MathSciNet review: 0283752
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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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DOI: https://doi.org/10.1090/S0002-9939-1971-0283752-5
Keywords: Non-Archimedean uniform space, ultrametric, uniform retract
Article copyright: © Copyright 1971 American Mathematical Society

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