M.Boshernitzan,

A dichotomy for projection of planar sets, preprint.

ABSTRACT

We prove that most one-dimensional projections of a discrete subset of R^2 are either dense in R, 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) of Lebesgue measure 0. The set E however does not need to be small in the sense of Hausdorff dimension. (12 pages.)

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