Geodesic
Measures of compactness in approach spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 2, pp. 327-345

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We investigate whether in the setting of approach spaces there exist measures of relative compactness, (relative) sequential compactness and (relative) countable compactness in the same vein as Kuratowski's measure of compactness. The answer is yes. Not only can we prove that such measures exist, but we can give usable formulas for them and we can prove that they behave nicely with respect to each other in the same way as the classical notions.
Classification : 54A05, 54E99
Keywords: approach space; compactness 
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Baekeland, R.; Lowen, R. Measures of compactness in approach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 2, pp. 327-345. http://geodesic.mathdoc.fr/item/CMUC_1995__36_2_a11/