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Abstract
We investigate the family 
of intersections of balls in a finite-dimensional vector space with a polyhedral norm. The spaces for which is closed under Minkowski addition are completely determined. We characterize also the polyhedral norms for which is closed under adding a ball. A subset 
of consists of the Mazur sets K, defined by the property that for any hyperplane H not meeting K there is a ball containing K and not meeting H. We characterize the Mazur sets in terms of their normal cones and also as summands of closed balls. As a consequence, we characterize the polyhedral spaces with only trivial Mazur sets as those whose unit ball is indecomposable.
Received: 2005-10-27
Published Online: 2007-06-28
Published in Print: 2007-07-20
© Walter de Gruyter
