Cardinal functions on modifications of uniform spaces and fine uniform spaces
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- by Věra Ku̇rková PDF
- Proc. Amer. Math. Soc. 84 (1982), 593-600 Request permission
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 $\alpha$).References
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Additional Information
- © Copyright 1982 American Mathematical Society
- 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