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On visibility and covering by convex sets

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Publication:1961351
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DOI10.1007/BF02780184zbMath0958.52008MaRDI QIDQ1961351

Ji{ří} Matoušek, Pavel Valtr

Publication date: 17 January 2000

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


zbMATH Keywords

coveringconvexvisibility\(n\)-convex


Mathematics Subject Classification ID

Variants of convex sets (star-shaped, ((m, n))-convex, etc.) (52A30)


Related Items (6)

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 three measures of non-convexity ⋮ Cantor-Bendixson degrees and convexity in \(\mathbb{R}^2\) ⋮ Convex decompositions in the plane and continuous pair colorings of the irrationals



Cites Work

  • A three point convexity property
  • A closed \((n+1)\)-convex set in \({\mathbb{R}}^ 2\) is a union of \(n^ 6\) convex sets
  • General decomposition theorems for m-convex sets in the plane
  • Sets in a Euclidean space which are not a countable union of convex subsets
  • Convexity and a certain property \(P_ m\)
  • A decomposition theorem for partially ordered sets
  • Finite Unions of Convex Sets
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