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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

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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