Steinhaus Sets and Jackson Sets

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We prove that there does not exist a subset of the plane S that meets every isometric copy of the vertices of the unit square in exactly one point. We give a complete characterization of all three point subsets F of the reals such that there does not exists a set of reals S which meets every isometric copy of F in exactly one point. A finite set X in the plane is Jackson iff for every subset S of the plane there exists an isometric copy Y of X such that Y does not meets S in exactly one point. These results are related to the open problem: Q. (Steve Jackson) Is every finite set X in the plane of two or more points Jackson?
Latex2e: 23 pages Latest version at http://www.math.wisc.edu/~miller

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Logic, Metric Geometry, 52C20, 05C12, 11H06

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http://salesiana.dossiersoluciones.com/handle/123456789/110136

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0603235
 http://arxiv.org/abs/math/0603235

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arXiv