On supercomplete spaces. III

Hohti, Aarno

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

On supercomplete spaces. III
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Proc. Amer. Math. Soc. 97 (1986), 339-342 Request permission

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.

References

Seymour Ginsburg and J. R. Isbell, Some operators on uniform spaces, Trans. Amer. Math. Soc. 93 (1959), 145–168. MR 112119, DOI 10.1090/S0002-9947-1959-0112119-4
Aarno Hohti, On supercomplete uniform spaces. II, Czechoslovak Math. J. 37(112) (1987), no. 3, 376–385. MR 904765

Products and uniform spaces

Uniform spaces

J. R. Isbell, Supercomplete spaces, Pacific J. Math. 12 (1962), 287–290. MR 156311
J. R. Isbell, Uniform spaces, Mathematical Surveys, No. 12, American Mathematical Society, Providence, R.I., 1964. MR 0170323
Teodor C. Przymusiński, On the notion of $n$-cardinality, Proc. Amer. Math. Soc. 69 (1978), no. 2, 333–338. MR 491191, DOI 10.1090/S0002-9939-1978-0491191-3