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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Coarse uniformities on the rationals


Author: H. C. Enos
Journal: Proc. Amer. Math. Soc. 34 (1972), 623-626
MSC: Primary 54E15
MathSciNet review: 0295283
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Abstract: There exist uniform spaces $ \mu Q$ homeomorphic with the space Q of rational numbers such that every homeomorphic uniform space admits a uniformly continuous homeomorphism upon $ \mu Q$. If ``homeomorphism'' is replaced by ``bijection", the resulting weaker property is equivalent to having as completion a Peano continuum. With ``homeomorphism", a (countable) dense subspace of a Hilbert cube has the property, but not a dense subspace of an interval.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0295283-8
Keywords: Uniformity, quotient space
Article copyright: © Copyright 1972 American Mathematical Society