Quantale-valued uniformizations of quantale-valued generalizations of approach groups by T. M. G. Ahsanullah and Gunther Jaeger
, T. M. G. Ahsanullah . 2019
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.
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