On supercomplete spaces. III

Hohti, Aarno

doi:10.1090/S0002-9939-1986-0835894-1

On supercomplete spaces. III
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by Aarno Hohti

Proc. Amer. Math. Soc. 97 (1986), 339-342

DOI: https://doi.org/10.1090/S0002-9939-1986-0835894-1

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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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