Necessary and sufficient conditions for hyperplane transversals
Authors: 
R. Pollack, R. WengerAuthors Info & Claims
R. Pollack, R. WengerAuthors Info & ClaimsPages 152 - 155
Abstract
We will prove that a finite family B = {B1, B2, …, Bn} of connected compact sets in Rd has a hyperplane transversal if and only if for some k there exists a set of points P = {P1, P2, …, Pn} (i.e. a k-dimensional labeling of the family) which spans Rk and every k + 2 sets of B are met by a k-flat consistent with the order type of P. This is a common generalization of theorems of Hadwiger, Katchalski, Goodman-Pollack and Wenger.
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Index Terms
- Necessary and sufficient conditions for hyperplane transversals
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Published: 05 June 1989
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