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 wellknown 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




00357596
 
DOI




10.1216/RMJM/1021477259
 
Volume/pages




30
:3
(2000)
, p. 10571073
 
ISI




000165670300018
 
Full text (Publisher's DOI)




 
