Showing papers by "Center for Discrete Mathematics and Theoretical Computer Science published in 1990"
TL;DR: It is proved that a finite family ℬ={B1,B2, ...,Bn} of connected compact sets in ℝd has a hyperplane transversal if and only if for somek there exists a set of pointsP which spans �”k and everyk+2 sets ofℬ are met by ak-flat consistent with the order type ofP.
Abstract: We prove that a finite family ℬ={B 1,B 2, ...,B n } of connected compact sets in ℝ d has a hyperplane transversal if and only if for somek there exists a set of pointsP={p 1,p 2, ...,p n } (i.e., ak-dimensional labeling of the family) which spans ℝ k and everyk+2 sets of ℬ are met by ak-flat consistent with the order type ofP. This is a common generalization of theorems of Hadwiger, Katchalski, Goodman-Pollack and Wenger.
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