We introduce the notions of Kuratowski-Ulam pairs of topological spaces and universally Kuratowski-Ulam space. A pair (X,Y) of topological spaces is called a Kuratowski-Ulam pair if the Kuratowski-Ulam Theorem holds in X× Y. A space Y is called a universally Kuratowski-Ulam (uK-U) space if (X,Y) is a Kuratowski-Ulam pair for every space X. Obviously, every meager in itself space is uK-U. Moreover, it is known that every space with a countable π-basis is uK-U. We prove the following: • every dyadic space (in fact, any continuous image of any product of separable metrizable spaces) is uK-U (so there are uK-U Baire spaces which do not have countable π-bases); • every Baire uK-U space is ccc.
@article{bwmeta1.element.bwnjournal-article-fmv165i3p239bwm,
author = {David Fremlin and Tomasz Natkaniec and Ireneusz Rec\l aw},
title = {Universally Kuratowski--Ulam spaces},
journal = {Fundamenta Mathematicae},
volume = {163},
year = {2000},
pages = {239-247},
zbl = {0959.54010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv165i3p239bwm}
}
Fremlin, David; Natkaniec, Tomasz; Recław, Ireneusz. Universally Kuratowski–Ulam spaces. Fundamenta Mathematicae, Tome 163 (2000) pp. 239-247. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv165i3p239bwm/
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