Necessary and sufficient conditions for hyperplane transversals

DOI10.1007/BF02122783zbMath0722.52005OpenAlexW2070830450MaRDI QIDQ756135

Rephael Wenger, Richard Pollack

Publication date: 1990

Published in: Combinatorica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02122783

zbMATH Keywords

hyperplane transversalBorsuk-Ulam theoremfamily of compact connected sets in \({\mathbb{R}}^ d\)k-ordering

Mathematics Subject Classification ID

Helly-type theorems and geometric transversal theory (52A35) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items

Flat transversals to flats and convex sets of a fixed dimension ⋮ A colorful theorem on transversal lines to plane convex sets ⋮ The colored Hadwiger transversal theorem in \(\mathbb{R}^d\) ⋮ A farewell to Ricky Pollack ⋮ Helly’s theorem: New variations and applications

Cites Work

• A generalization of Hadwiger's transversal theorem to intersecting sets
• Thin sets and common transversals
• On a theorem of L. A. Santaló
• Multidimensional Sorting
• Hadwiger's Transversal Theorem In Higher Dimensions
• Characterizations of Radon partitions
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