English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

We investigate the familyof intersections of balls in a finite-dimensional vector space with a polyhedral norm. The spaces for whichis closed under Minkowski addition are completely determined. We characterize also the polyhedral norms for whichis closed under adding a ball. A subsetofconsists 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.

Intersection properties of polyhedral norms