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A closed \((n+1)\)-convex set in \({\mathbb{R}}^ 2\) is a union of \(n^ 6\) convex sets

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Publication:919620
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DOI10.1007/BF02801466zbMath0707.52002OpenAlexW1991697811MaRDI QIDQ919620

Saharon Shelah, Micha A. Perles

Publication date: 1990

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02801466


zbMATH Keywords

convex sets


Mathematics Subject Classification ID

Convex sets in (2) dimensions (including convex curves) (52A10)


Related Items (8)

Finite sets as complements of finite unions of convex sets ⋮ Convex decompositions and the valence of some functions ⋮ A planar 3-convex set is indeed a union of six convex sets ⋮ On visibility and covering by convex sets ⋮ On three measures of non-convexity ⋮ Cantor-Bendixson degrees and convexity in \(\mathbb{R}^2\) ⋮ Sets in a Euclidean space which are not a countable union of convex subsets ⋮ Convex decompositions in the plane and continuous pair colorings of the irrationals



Cites Work

  • A three point convexity property
  • General decomposition theorems for m-convex sets in the plane
  • On Unions of Two Convex Sets
  • Unnamed Item


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