Nearly all convex bodies are smooth and strictly convex
type: Item
instance of: scholarly article
title: Nearly all convex bodies are smooth and strictly convex
zbMATH Open document ID: 0607.52002
DOI: 10.1007/BF01302711
published in: Monatshefte für Mathematik
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178314
review text: 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.
Mathematics Subject Classification ID: 52A05
Mathematics Subject Classification ID: 28A05
zbMATH DE Number: 3981966
zbMATH Keywords: convex bodies
zbMATH Keywords: \(\sigma \)-porous set
author: Tudor Zamfirescu
MaRDI profile type: Publication
cites work: Q5593766
cites work: Q3689014
cites work: Some new results on smoothness and rotundity in normed linear spaces
cites work: Many endpoints and few interior points of geodesics
cites work: Points of infinitely many normals to convex surfaces.
cites work: Q3736454
description: scientific article; zbMATH DE number 3981966