Cutting families of convex sets
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- by Meir Katchalski and Ted Lewis PDF
- Proc. Amer. Math. Soc. 79 (1980), 457-461 Request permission
Abstract:
A family of convex sets in the plane admits a common transversal if there is a straight line which intersects (cuts) each member of the family. It is shown that there is a positive integer k such that for any compact convex set C in the plane and for any finite family $\mathcal {A}$ of pairwise disjoint translates of C: If each 3-membered subfamily of $\mathcal {A}$ admits a common transversal then there is a subfamily $\mathcal {B}$ of $\mathcal {A}$ such that $\mathcal {B}$ admits a common transversal and $|\mathcal {A}\backslash \mathcal {B}| \leqslant k$.References
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Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 79 (1980), 457-461
- MSC: Primary 52A35; Secondary 52A10
- DOI: https://doi.org/10.1090/S0002-9939-1980-0567992-9
- MathSciNet review: 567992