Quantale-valued generalizations of approach convergence groups

Journal Article
Jaeger, T.M.G. Ahsanullah and Gunther . 2019
Publication Work Type: 
Original Reserach
Magazine \ Newspaper: 
New Math and Natural Computation
Issue Number: 
1
Volume Number: 
15
Pages: 
1-30
Publication Abstract: 

The motive behind this article is to generalize the concept of approach groups. In so doing, we introduce various categories, specifically, the categories of quantale-valued convergence groups, quantale-valued approach groups, quantale-valued gauge groups and quantale-valued approach system groups, and study their functorial relationships including the fact that theĀ  category of quantale-valued gauge groups as well as the category of quantale-valued approach system groups is topological over the category of groups. Besides obtaining a variety of categorical connections, we note that if the quantale is linearly ordered satisfying certain conditions, then the categories of quantale-valued approach system groups and quantale-valued gauge groups are isomorphic. Finally, we look into the embeddings of the category of quantale-valued metric groups into the categories of quantale-valued generalizations of approach groups including commutativity of some diagrams.