Cardinal functions on modifications of uniform spaces and fine uniform spaces

Author:
Věra Kurková

Journal:
Proc. Amer. Math. Soc. **84** (1982), 593-600

MSC:
Primary 54E15; Secondary 54B30

DOI:
https://doi.org/10.1090/S0002-9939-1982-0643756-4

MathSciNet review:
643756

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Abstract: The paper studies the question for which modifications of Unif the following theorem can be generalized by substituting a precompact modification by : A uniform space has the finest uniformity inducing its proximity if and only if each proximally continuous mapping from this space to any other uniform space is uniformly continuous. By means of two cardinal functions defined on the class of all modifications of Unif there is shown that this is possible only for cardinal modifications . Assuming GCH, the problem for cardinal modifications is solved for uniform spaces of a limited point-character (in dependence on ).

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DOI:
https://doi.org/10.1090/S0002-9939-1982-0643756-4

Keywords:
Uniform space,
modification,
cardinal modification,
point-character

Article copyright:
© Copyright 1982
American Mathematical Society