- Tytuł:
- Universally Kuratowski–Ulam spaces
- Autorzy:
-
Fremlin, David
Natkaniec, Tomasz
Recław, Ireneusz - Powiązania:
- https://bibliotekanauki.pl/articles/1205007.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Baire space
dyadic space
quasi-dyadic space
Kuratowski-Ulam Theorem
Kuratowski-Ulam pair
universally Kuratowski-Ulam space - Opis:
-
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. - Źródło:
-
Fundamenta Mathematicae; 2000, 165, 3; 239-247
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł