Balanced Topological Groups
by
G. L. Itzkowitz
Queens College

A survey and some history will be given of the following question concerning topological groups: Does the class of SIN groups and the class of FSIN groups coincide? A topological group G is said to be a SIN group if the left and right uniform structures on G coincide. A topological group G is said to be an FSIN group (functionally SIN) if the class of right uniformly continuous real-valued functions on G coincides with the class of left uniformly continuous real-valued functions. Earlier results(1970-74) were concerned with the solution of the problem for the locally compact metrizable and unimodular cases. More recently, during the period 1990-92 the question was answered in the affirmative and independently by a number of authors for the locally compact case. At the present time, extensions of these results have been obtained by various authors for classes of topological groups that are not locally compact (including more general classes). The survey will include some of the new results.

Date received: March 14, 1997

Copyright © 1997 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 # caam-55.