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AUnif: A common supercategory of pMET and Unif. (English) Zbl 0890.54024
Although the first author’s approach spaces [Approach spaces: the missing link in the topology-uniformity-metric triad, Oxford Mathematical Monographs, Oxford (1997)] involve uniform ideas from their origin, it seems that the uniformity is insufficient. “…the theory is local. For instance, the space of continuous functions between metric spaces” with a natural approach structure is always complete. “Also, AP seems not to be the right context for the quantification of uniform properties …”. This has motivated the authors to introduce new ‘approach uniformities’, whose theory this paper initiates.

MSC:
54E15 Uniform structures and generalizations
54B30 Categorical methods in general topology
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