Abstract

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.

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Keywords

  • Intersection of balls
  • Mazur intersection property
  • Mazur set
  • semidenting point
  • weak* denting point

Mathematics Subject Classification

46B20; 46B26, 60D05

Suggested citation

P. Terán. “Intersections of Balls and the Ball Hull Mapping.” Journal of Convex Analysis 17 (2010), No. 1, 277–292. https://doi.org/10.68381/jca17020

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Published by Heldermann Verlag, 2010. Rights now held by Banach Press.