Universally Kuratowski-Ulam spaces
by
Ireneusz Reclaw
University of Gdansk
Coauthors: David Fremlin, Tomasz Natkaniec

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 Kuratowski-Ulam pair if the Kuratowski-Ulam Theorem holds in X ×Y i.e. if E in M(X ×Y), then { x in X : E_x not in M(Y) } in M(X). A space Y is called universally Kuratowski-Ulam 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 \pi-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 \pi-bases);
• every Baire uK-U space is ccc.

http://math.univ.gda.pl/~rp/i.reclaw

Date received: March 1, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cady-69.