Geodesic
On the quantification of uniform properties
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 4, pp. 749-759.

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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.
Classification : 54B30, 54E15, 54E35
Keywords: uniform space; approach uniform space; totally bounded; precompact; complete; measure of total boundedness; measure of completeness 
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Lowen, R.; Windels, B. On the quantification of uniform properties. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 4, pp. 749-759. http://geodesic.mathdoc.fr/item/CMUC_1997__38_4_a10/