On the axiomatization of convex subsets of Banach spaces (Q2838969)
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scientific article; zbMATH DE number 6183792
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the axiomatization of convex subsets of Banach spaces |
scientific article; zbMATH DE number 6183792 |
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On the axiomatization of convex subsets of Banach spaces (English)
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4 July 2013
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convex-like structure
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Stone's barycentric calculus
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convex space
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In this paper, the authors identify a set of axioms (Brown's algebraic axioms) defined on the \(n\)-fold Cartesian product of a complete metric space \(X\) as axioms of a convex like structure defined on a non-empty set and characterize such convexity spaces using these axioms. In particular, the authors axiomatically characterize the convex subsets of a Banach space.NEWLINENEWLINENEWLINEThe paper is an interesting contribution to axiomatic and abstract convexity.
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