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uniform space; approach uniform space; totally bounded; precompact; complete; measure of total boundedness; measure of completeness
Approach spaces ([4], [5]) turned out to be a natural setting for the quantification of topological properties. Thus a measure of compactness for approach spaces generalizing the well-known Kuratowski measure of non-compactness for metric spaces was defined ([3]). This article shows that approach uniformities (introduced in [6]) have the same advantage with respect to uniform concepts: they allow a nice quantification of uniform properties, such as total boundedness and completeness.
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[5] Lowen R.: Approach Spaces: the Missing Link in the Topology-Uniformity-Metric Triad. Oxford Mathematical Monographs, Oxford University Press, 1997. MR 1472024 | Zbl 0891.54001
[6] Lowen R., Windels B.: AUnif, a common supercategory of pMET and Unif. to appear in Int. J. Math. Math. Sci. MR 1486952 | Zbl 0890.54024
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