Sets in a Euclidean space which are not a countable union of convex subsets

DOI10.1007/BF02801467zbMath0742.52002OpenAlexW2064755890MaRDI QIDQ1814005

Saharon Shelah, Micha A. Perles, Menachem Kojman

Publication date: 25 June 1992

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

Full work available at URL: https://doi.org/10.1007/bf02801467

zbMATH Keywords

planar setnot a countable union of convex subsets

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Asymptotic enumeration (05A16) Convex sets in (2) dimensions (including convex curves) (52A10)

Related Items (7)

Analytic colorings ⋮ On visibility and covering by convex sets ⋮ On three measures of non-convexity ⋮ More on convexity numbers of closed sets in ℝⁿ ⋮ Cantor-Bendixson degrees and convexity in \(\mathbb{R}^2\) ⋮ Geometric Cardinal Invariants, Maximal Functions and a Measure Theoretic Pigeonhole Principle ⋮ Convex decompositions in the plane and continuous pair colorings of the irrationals

Cites Work

• A closed \((n+1)\)-convex set in \({\mathbb{R}}^ 2\) is a union of \(n^ 6\) convex sets
• A Construction of Graphs without Triangles having Pre-Assigned Order and Chromatic Number

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