Locally nonconical convexity (Q2718686)
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scientific article; zbMATH DE number 1596895
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Locally nonconical convexity |
scientific article; zbMATH DE number 1596895 |
Statements
4 June 2001
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locally nonconical convex set
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continuous section
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continuous selection
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strictly convex
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zonoid
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0.92885685
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0.9053608
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Locally nonconical convexity (English)
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Locally nonconical convexity is a generalization of strict convexity. The authors study this concept and its relations to the existence of continuous sections (selections). For a linear map \(T:R^n\to R^m\) and a convex set \(Q\) a section is a right inverse map from \(T(Q)\) into \(Q\). Continuous sections are constructed in various natural ways. Analogous results are found for Hilbert spaces if \(T\) is left Fredholm, i.e. is a bounded linear map with closed range and finite-dimensional kernel.
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