Coarse uniformities on the rationals
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- by H. C. Enos PDF
- Proc. Amer. Math. Soc. 34 (1972), 623-626 Request permission
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.References
- M. K. Fort Jr., Homogeneity of infinite products of manifolds with boundary, Pacific J. Math. 12 (1962), 879–884. MR 145499
- J. R. Isbell, Uniform spaces, Mathematical Surveys, No. 12, American Mathematical Society, Providence, R.I., 1964. MR 0170323
- S. Mrówka, Continuous functions on countable subspaces, Portugal. Math. 29 (1970), 177–180. MR 293605
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 34 (1972), 623-626
- MSC: Primary 54E15
- DOI: https://doi.org/10.1090/S0002-9939-1972-0295283-8
- MathSciNet review: 0295283