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A Lindelöf topological group whose square is not normal
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 Sorgenfrey line (clearly, the square of such a group is not normal). We construct a ZFC example of a Lindelöf topological group whose square is not normal and prove that a normal topological group cannot contain a closed copy of Sorgenfrey line.
Date received: June 4, 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 Mathematical Conference Abstracts. Document # cajv-59.