Balance, Functional Balance, and Discrete balance in Topological groups
by
Gerald Itzkowitz
Queens College/C.U.N.Y.

A new characterization of balanced topological groups will be discussed. This characterization makes use of the concept of discrete balance that was introduced by T.S. Wu in a question to the author. A topological group is discretely balanced if every left uniformly discrete subset is right uniformly discrete. The proof of this new result makes use of a theorem on extending uniformly continuous functions on a uniform space. This theorem is a consequence of Katetov's well known theorem on extending such functions and a previous characterization of uniform separation of sets in uniform spaces that appeared in a paper by the author in the Proceedings Of The Summer Topology Conference At Slippery Rock in 1993. Finally some interesting corollaries of the main result will be discussed.

Date received: May 24, 2001

Copyright © 2001 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 # cagw-82.