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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 $ r$ of Unif the following theorem can be generalized by substituting a precompact modification $ p$ by $ r$: 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 $ {p^\alpha }$. Assuming GCH, the problem for cardinal modifications $ {p^\alpha }$ is solved for uniform spaces of a limited point-character (in dependence on $ \alpha $).


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Additional Information

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