Universally Kuratowski–Ulam spaces

• Autorzy: David H. Fremlin , Tomasz Natkaniec , Ireneusz Recław
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 54E52: Baire category, Baire spaces
• 54B10: Product spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2000
• Tom: 165
• Numer: 3
• Strony: 239-247

Daty

wydano

2000

otrzymano

1999-12-06

poprawiono

2000-06-19

Twórcy

autor

David H. Fremlin

• Mathematics Department, University of Essex, Colchester CO4 3SQ, England

autor

Tomasz Natkaniec

• Department of Mathematics, Gdańsk University, Wita Stwosza 57, 80-952 Gdańsk, Poland

autor

Ireneusz Recław

• Department of Mathematics, Gdańsk University, Wita Stwosza 57, 80-952 Gdańsk, Poland

Bibliografia

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