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
 
Volume/pages 



30:3(2000), p. 10571073
 
ISI 



000165670300018
 
Full text (Publishers DOI) 


  
