AUnif: A common supercategory of pMET and Unif (Q1380946)

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. ``\dots the theory is local. For instance, the space of continuous functions between metric spaces'' with a natural approach structure is always complete. ``Also, \textbf{AP} seems not to be the right context for the quantification of uniform properties \dots''. This has motivated the authors to introduce new `approach uniformities', whose theory this paper initiates.