Publication
Title
Approach groups
Author
Abstract
 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 knowthat this 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 contraction. Examples showth at different well-known topological (semi-)groups can be equipped with a natural metric (or gauge of metrics) such that addition is contractive. 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 with the classical concept. For instance, every approach group allows for a natural uniformization.
Language
English
Source (journal)
The Rocky Mountain journal of mathematics. - Provo, Utah
Publication
Provo, Utah : 2000
ISSN
0035-7596
Volume/pages
30:3(2000), p. 1057-1073
ISI
000165670300018
Full text (Publishers DOI)
UAntwerpen
 Faculty/Department Research group Publication type Subject Affiliation Publications with a UAntwerp address