Quantale-valued uniformizations of quantale-valued generalizations of approach groups

Journal Article
Jaeger, T. M. G. Ahsanullah and Gunther . 2019
Publication Work Type: 
Original Reserach
Magazine \ Newspaper: 
New Mathematics and Natural Computations
Issue Number: 
3
Volume Number: 
15
Pages: 
517 to 538
Publication Abstract: 

We introduce the categories of quantale-valued approach uniform spaces and quantale-valued uniform gauge spaces, and prove that they are topological categories. We first show that the category of quantale-valued uniform gauge spaces is a reflective subcategory of the category of quantale-valued approach uniform spaces and, second,we prove that only under strong restrictions on the quantale these two categories are isomorphic. Besides presenting embeddings of the category of quantale-valuedmetric spaces into the categories of quantale-valued approach uniform spaces as well as quantale-valued uniform gauge spaces, we show that every quantale-valued approach system group and quantale-valued gauge group has a natural underlying quantale-valued approach uniform space, respectively, a quantale-valued unifor gauge space.