A dichotomy for projections of planar sets
Metric Geometry
2012-03-06 v1 Combinatorics
Dynamical Systems
Number Theory
Abstract
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.
Cite
@article{arxiv.1203.0669,
title = {A dichotomy for projections of planar sets},
author = {Michael Boshernitzan},
journal= {arXiv preprint arXiv:1203.0669},
year = {2012}
}
Comments
11 pages