Necessary and sufficient conditions for hyperplane transversals
type: Item
instance of: scholarly article
title: Necessary and sufficient conditions for hyperplane transversals
zbMATH Open document ID: 0722.52005
DOI: 10.1007/BF02122783
author: Rephael Wenger
author: Richard Pollack
published in: Combinatorica
publication date: 1990-01-01T00:00:00Z
review text: By applying the Borsuk-Ulam theorem the authors prove that a family of compact connected sets in \({\mathbb{R}}^ d\) has a hyperplane transversal if and only if for some \(k\in [0,d-1]\) there is a non-trivial k-ordering of the family such that every \(k+2\) sets are intersected by some oriented k- flat consistent with the k-ordering.
Mathematics Subject Classification ID: 52A35
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 4190573
zbMATH Keywords: Borsuk-Ulam theorem
zbMATH Keywords: family of compact connected sets in \({\mathbb{R}}^ d\)
zbMATH Keywords: hyperplane transversal
zbMATH Keywords: k-ordering
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02122783
OpenAlex ID: W2070830450
description: scientific article; zbMATH DE number 4190573