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Set Theory, Topology and Banach Spaces (Second International Topology Conference in Kielce)
July 7-11, 2008
Institute of Mathematics, Jan Kochanowski University in Kielce; co-organized by Technical University of Lodz
Kielce, Poland

Organizers
Taras Banakh, Piotr Koszmider, Wieslaw Kubis

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On antipower functors
by
Leonid Shapiro
Academy of Labor and Social Relations, ul.Lobachevskogo 90, 119454 Moscow, Russia

A compactum is a compact Hausdorff space. Given a compactum X let H(X) (respectively, P(X)) denote the family of all nonempty closed subsets of X (probability measures on X) equipped with Vietoris (weak*) topology.

The main result is the following

Theorem.   If t is an uncountable cardinal and H(X) (respectively, P(X)) is a continuous image of the product ∏Xs s.t. w(Xs) ≤ t for any s, then w(X) ≤ t.

In the talk, this result is generalized to the subclass of normal functors called antipower functors.

Date received: June 23, 2008

Copyright © 2008 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 # caxg-14.