Group topologies for the subgroups and quotient groups of R^\omega that make the arc component of the identity dense
by
Jon W. Short
Saint Louis University

I will discuss a procedure for constructing metrizable group topologies on the subgroups and quotient groups of R^\omega that are weaker than the standard topologies. With these topologies, each group will contain a dense, weakened analytic group (a group obtained by weakening the topology on a connected Lie group). For example, I will construct a metrizable group topology on R×(Z_n)^\omega that is connected and not arcwise connected, but in which the arc component of the identity is dense. Other ``unusual'' properties of these topological groups will be discussed. Topological groups containing a dense, weakened analytic group arise in the study of topological transformation groups and in determining when these transformation groups are in fact Lie groups.

Date received: July 4, 2000

Copyright © 2000 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 # caeu-58.