Journal of Convex Analysis 17 (2010), No. 1, 277--292
Copyright Heldermann Verlag 2010
Intersections of Balls and the Ball Hull Mapping
Pedro Terán
Dep de Estadística, Universidad de Oviedo, 33071 Gijón, Spain
pedro.teran@gmail.com
We are concerned with some properties of the family of all subsets of a Banach space that can be written as an intersection of balls. A space with the Mazur Intersection Property (MIP) always satisfies those properties, so they can be regarded as weakenings of the MIP in different directions. The "ball hull" function (mapping a set to the intersection of all closed balls that cover it) is often an effective tool to study those properties.
Keywords: Intersection of balls, Mazur intersection property, Mazur set, semidenting point, weak* denting point.
MSC: 46B20; 46B26, 60D05
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