Nearly all convex bodies are smooth and strictly convex (Q1085437)
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scientific article; zbMATH DE number 3981966
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nearly all convex bodies are smooth and strictly convex |
scientific article; zbMATH DE number 3981966 |
Statements
Nearly all convex bodies are smooth and strictly convex (English)
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1987
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By an old result of \textit{V. Klee} [Math. Ann. 139, 51-63 (1959; Zbl 0092.116)], those convex bodies which are not smooth or not strictly convex form a set of first Baire category. It is proved here that they are ''even fewer'': they only form a \(\sigma\)-porous set.
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convex bodies
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\(\sigma \)-porous set
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