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2003 Summer Conference on Topology and its Applications
July 9-12, 2003
Howard University
Washington, DC, USA

Organizers
Neil Hindman, Joshua Leslie, Amir Maleki, Thierry Robart, Sherif El-Helaly, John Kulesza, Salvador Garcia-Ferreira, Javier Trigos-Arrietta, Grant Woods, Alan Dow, Judy Kennedy, Randall McCutcheon Karl Hofmann, Dona Strauss, Jimmie Lawson, Michael Mislove

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Normality and the Lindelöf property in products of topological groups
by
Oleg Pavlov
Mercer University

Various authors constructed consistent examples of normal topological groups whose squares are not normal and of Lindelöf topological groups whose squares are not Lindelöf. A. V. Arhangel'skii asked whether such examples are possible in ZFC and whether there is a ZFC normal or Lindelöf topological group which contains a closed copy of the Sorgenfrey line (clearly, the square of such a group is not normal). For every natural number n, we construct a topological group G in ZFC such that Gn is Lindelöf and Gn+1 is not normal. Also, we prove that a normal topological group cannot contain a closed copy of the Sorgenfrey line.

Date received: June 18, 2003

Copyright © 2003 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 # calv-08.