# Universally Kuratowski–Ulam spaces

David Fremlin; Tomasz Natkaniec; Ireneusz Recław

Fundamenta Mathematicae (2000)

- Volume: 165, Issue: 3, page 239-247
- ISSN: 0016-2736

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topFremlin, David, Natkaniec, Tomasz, and Recław, Ireneusz. "Universally Kuratowski–Ulam spaces." Fundamenta Mathematicae 165.3 (2000): 239-247. <http://eudml.org/doc/212468>.

@article{Fremlin2000,

abstract = {
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.
},

author = {Fremlin, David, Natkaniec, Tomasz, Recław, Ireneusz},

journal = {Fundamenta Mathematicae},

keywords = {Baire space; dyadic space; quasi-dyadic space; Kuratowski-Ulam Theorem; Kuratowski-Ulam pair; universally Kuratowski-Ulam space; Kuratowski-Ulam theorem},

language = {eng},

number = {3},

pages = {239-247},

title = {Universally Kuratowski–Ulam spaces},

url = {http://eudml.org/doc/212468},

volume = {165},

year = {2000},

}

TY - JOUR

AU - Fremlin, David

AU - Natkaniec, Tomasz

AU - Recław, Ireneusz

TI - Universally Kuratowski–Ulam spaces

JO - Fundamenta Mathematicae

PY - 2000

VL - 165

IS - 3

SP - 239

EP - 247

AB -
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.

LA - eng

KW - Baire space; dyadic space; quasi-dyadic space; Kuratowski-Ulam Theorem; Kuratowski-Ulam pair; universally Kuratowski-Ulam space; Kuratowski-Ulam theorem

UR - http://eudml.org/doc/212468

ER -

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