Geodesic
Universally Kuratowski–Ulam spaces
Fundamenta Mathematicae, Tome 165 (2000) no. 3, pp. 239-247.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm-165-3-239-247
Keywords: Baire space, dyadic space, quasi-dyadic space, Kuratowski-Ulam Theorem, Kuratowski-Ulam pair, universally Kuratowski-Ulam space

David Fremlin 1 ; Tomasz Natkaniec 1 ; Ireneusz Recław 1

1 
@article{10_4064_fm_165_3_239_247,
     author = {David Fremlin and Tomasz Natkaniec and Ireneusz Rec{\l}aw},
     title = {Universally {Kuratowski{\textendash}Ulam} spaces},
     journal = {Fundamenta Mathematicae},
     pages = {239--247},
     publisher = {mathdoc},
     volume = {165},
     number = {3},
     year = {2000},
     doi = {10.4064/fm-165-3-239-247},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-165-3-239-247/}
}
TY  - JOUR
AU  - David Fremlin
AU  - Tomasz Natkaniec
AU  - Ireneusz Recław
TI  - Universally Kuratowski–Ulam spaces
JO  - Fundamenta Mathematicae
PY  - 2000
SP  - 239
EP  - 247
VL  - 165
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm-165-3-239-247/
DO  - 10.4064/fm-165-3-239-247
LA  - en
ID  - 10_4064_fm_165_3_239_247
ER  - 
%0 Journal Article
%A David Fremlin
%A Tomasz Natkaniec
%A Ireneusz Recław
%T Universally Kuratowski–Ulam spaces
%J Fundamenta Mathematicae
%D 2000
%P 239-247
%V 165
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/fm-165-3-239-247/
%R 10.4064/fm-165-3-239-247
%G en
%F 10_4064_fm_165_3_239_247
David Fremlin; Tomasz Natkaniec; Ireneusz Recław. Universally Kuratowski–Ulam spaces. Fundamenta Mathematicae, Tome 165 (2000) no. 3, pp. 239-247. doi : 10.4064/fm-165-3-239-247. http://geodesic.mathdoc.fr/articles/10.4064/fm-165-3-239-247/

Cité par Sources :