On uniformly continuous functions between pseudometric spaces and the Axiom of Countable Choice View Full Text


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Article Info

DATE

2019-05

AUTHORS

Samuel G. da Silva

ABSTRACT

In this note we show that the Axiom of Countable Choice is equivalent to two statements from the theory of pseudometric spaces: the first of them is a well-known characterization of uniform continuity for functions between (pseudo)metric spaces, and the second declares that sequentially compact pseudometric spaces are UC—meaning that all real valued, continuous functions defined on these spaces are necessarily uniformly continuous. More... »

PAGES

353-358

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00153-018-0643-2

DOI

http://dx.doi.org/10.1007/s00153-018-0643-2

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1105642702


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