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IV Iberoamerican Conference on Topology and its Applications (IV CITA)
April 18-21, 2001
University of Coimbra
Coimbra, Portugal

Organizers
Maria Manuel Clementino, Jorge Picado, Lurdes Sousa, Maria João Ferreira, Gonçalo Gutierres, Dirk Hofmann

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Topological characterization of equivalent uniformities in topological groups
by
Salvador Hernández
Universitat Jaume I

We characterize the topological groups with equivalent left and right uniform structures (SIN groups) by means of their uniformly discrete subsets. As a consequence, it follows that a \aleph0 -bounded non-Archimedean group G is SIN if and only if every left uniformly continuous real-valued function on G is right uniformly continuous. And, in general, a topological group is SIN if and only if every set of left (right) equiuniformly real-valued functions on G is right (left) equiuniformly continuous.

Date received: March 6, 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 # cafw-60.