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Spring Topology and Dynamics Conference
March 21-23, 2002
University of Texas
Austin, TX, USA

Organizers
Cameron Gordon, John Luecke, Alan Reid

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Local Isometries of Weakened Topologies
by
Jon W. Short
Sam Houston State University
Coauthors: T. Christine Stevens (Saint Louis University)

A weakened Lie group (WL-group) is topological group obtained by weakening the topology of a Lie group. We will discuss a constructive procedure for obtaining WL-groups which are separable, metrizable, and (most of the time) finite dimensional. Even though many nonhomeomorphic group topologies arise by this method, our main result shows that the topologies are, with small restrictions, locally isometric. A similar result is true for the completions of the topological groups. Examples of ``interesting'' topologies obtained by this method will also be discussed.

Date received: March 1, 2002

Copyright © 2002 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 # caik-80.