A dichotomy for projections of planar sets

Details A dichotomy for projections of planar sets A dichotomy for projections of planar sets

2012-03-03

arxiv.org/abs/1203.0669v1

Mathematics

Metric Geometry

11 pages

Scientific paper

We prove that most one-dimensional projections of a discrete subset of a plane are either dense in R (the real line), or form a discrete subset of R. More precisely, the set E of exceptional directions (for which the indicated dichotomy fails) is a meager subset of the unit circle T of Lebesgue measure 0. The set E however does not need to be small in the sense of Hausdorff dimension.

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