Line Transversals to Translates of Unit Discs |
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Authors: | Jesus Jeronimo Castro |
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Affiliation: | (1) Centro de Investigacion en Matematicas, Guanajuato, Gto., C.P. 36000, Mexico |
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Abstract: | Let be a family of convex figures in the plane. We say that has property T if there exists a line intersecting every member of . Also, the family has property T(k) if every k-membered subfamily of has property T. Let B be the unit disc centered at the origin. In this paper we prove that if a finite family of translates of B has property T(4) then the family , where , has property T. We also give some results concerning families of translates of the unit disc which has either property T(3) or property T(5). |
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