More than just topological groups
by
Bart Windels
University of Antwerp
Coauthors: Robert Lowen

Any normed vector space X is a topological group with respect to the norm topology and the underlying group operation of the vector space. Although for the majority of applications it is sufficient to know that the group operation + : X ×X --> X : (x, y) --> x+y is continuous, stronger properties of this mapping can be shown. In fact, if X ×X is equipped with the sum product metric, then addition becomes a non-expansive map. Examples show that different well-known topological (semi-)groups can be equipped with a natural metric (or gauge of metrics) such that addition is contractive in a suitable sense. This approach group structure is a canonical generalization of topological groups (or metric groups in the sense of Parthasarathy), and shares some of the important features of the classical concept. For instance, every approach group allows for a natural uniformization.

Date received: June 10, 1998

Copyright © 1998 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 # cabc-24.