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Proceedings of the American Mathematical Society

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On supercomplete spaces. III


Author: Aarno Hohti
Journal: Proc. Amer. Math. Soc. 97 (1986), 339-342
MSC: Primary 54E15
DOI: https://doi.org/10.1090/S0002-9939-1986-0835894-1
MathSciNet review: 835894
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Abstract: We show that for each positive integer $ n$ there is a fine uniform space $ X$, topologically a subspace of the real line, such that $ {X^n}$ is supercomplete, but $ {X^{n + 1}}$ is not supercomplete. The space $ X$ can also be chosen so that that $ {X^n}$ is supercomplete for all $ n \in N$, but the countably infinite power $ {X^N}$ is not supercomplete.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0835894-1
Keywords: Supercomplete, locally fine coreflection, fine space, $ n$-cardinality
Article copyright: © Copyright 1986 American Mathematical Society