A closed \((n+1)\)-convex set in \({\mathbb{R}}^ 2\) is a union of \(n^ 6\) convex sets
type: Item
instance of: scholarly article
title: A closed \((n+1)\)-convex set in \({\mathbb{R}}^ 2\) is a union of \(n^ 6\) convex sets
zbMATH Open document ID: 0707.52002
DOI: 10.1007/BF02801466
author: S. Shelah
author: Micha A. Perles
published in: Israel Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: It is shown that if a closed set S in the plane is \(n+1\)-convex, then it has no more than \(n^ 4\) holes. As a consequence, it can be covered by \(\leq n^ 6\) convex subsets. This is an improvement on the bound of \(2^ n\cdot n^ 3\) obtained by \textit{M. Breen} and \textit{D. C. Kay} [Israel J. Math. 24, 217-233 (1976; Zbl 0342.52006)].
Mathematics Subject Classification ID: 52A10
zbMATH DE Number: 4161569
zbMATH Keywords: convex sets
MaRDI profile type: Publication
cites work: General decomposition theorems for m-convex sets in the plane
cites work: Q4768277
cites work: On Unions of Two Convex Sets
cites work: A three point convexity property
full work available at URL: https://doi.org/10.1007/bf02801466
OpenAlex ID: W1991697811
description: scientific article; zbMATH DE number 4161569