Fine uniformity and the locally finite hyperspace topology
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- by S. A. Naimpally and P. L. Sharma
- Proc. Amer. Math. Soc. 103 (1988), 641-646
- DOI: https://doi.org/10.1090/S0002-9939-1988-0943098-9
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Abstract:
It is shown that a uniformizable space $X$ is normal iff the locally finite topology ${e^\tau }$ on the hyperspace ${2^X}$ coincides with the topology transmitted by the fine uniformity of $X$. We also prove that, for $X$ normal, the topology ${e^\tau }$ is first countable only if the set of limit points $X’$ of $X$ is countably compact. Applications of these results to pseudocompactness and Atsuji spaces are given.References
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Bibliographic Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 641-646
- MSC: Primary 54B20; Secondary 54D30, 54E15
- DOI: https://doi.org/10.1090/S0002-9939-1988-0943098-9
- MathSciNet review: 943098