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Baire irresolvable spaces and ideal theory. (English) Zbl 0613.54018

Pr. Nauk. Uniw. Śląsk. Katowicach 752, Ann. Math. Silesianae 2(14), 98-107 (1986).
The paper deals with a Katětov problem about the existence of a (Hausdorff) space without isolated points such that every real-valued function on that space is continuous in at least one point. It is shown that the existence of such a space is equivalent to the existence of an \(\omega\)-complete ideal I over a cardinal \(\kappa\) with a family which is both I-dense and I-proper, which, in turn, is equiconsistent to the existence of measurable cardinal.
Reviewer: A.Szymański

MSC:

54E52 Baire category, Baire spaces
54A35 Consistency and independence results in general topology