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The Spring Topology and Dynamics Conference 2009
March 7-9, 2009
University of Florida
Gainesville, FL, USA

Organizers
Lou Block, Phil Boyland (chair), Beverly Brechner, Sasha Dranishnikov, and Jed Keesling.

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Cardinality bounds of H-sets in Urysohn spaces
by
Daniel McNeill
University of Kansas

A Urysohn space X is constructed which has an H-set A with |A| > 2pc(X), where pc(X) is the closed-pseudocharacter of the space X. The space provides a counterexample to a question of Fedeli. In addition, there is no theta-continuous map from a compact Hausdorff space to the space X with the H-set A as the image, giving a Urysohn counterexample to a conjecture of Vermeer. Finally, it is shown that the cardinality of an H-set in a Urysohn space X is bounded by 2c(Xs), where c(X) is the character of X and Xs is the semiregularization of X. This refines a result of Bella stating that the cardinality of such an H-set is bounded by 2c(X).

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Date received: January 26, 2009

Copyright © 2009 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 # caxy-23.