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• W2022028013 abstract "In this paper we aim to investigate different questions concerning the stability of the set M of all intersections of closed balls in a normed space. We are mainly concerned with: (i) the stability of M under the closure of the vector sums; (ii) the stability under the addition of balls. We prove that (i) and (ii) are different properties which have strong connections with the geometry of the space. They have interest both in finite and infinite dimension. In the former case, there is a link with linear programming theory. We also study two more stability properties related to the well-known binary intersection property. Mazur sets and Mazur spaces are introduced, as a natural family satisfying (i). We prove that every two-dimensional normed space is a Mazur space, a result which distinguishes dimension d⩽2 from dimension d⩾3. We also discuss the connections between Mazur spaces and porosity." @default.
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• W2022028013 date "2004-03-01" @default.
• W2022028013 modified "2023-10-03" @default.
• W2022028013 title "Convex sets which are intersections of closed balls" @default.
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• W2022028013 doi "https://doi.org/10.1016/s0001-8708(03)00086-0" @default.
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