Stripes on rectangular tilings

Details Stripes on rectangular tilings Stripes on rectangular tilings

2011-01-16

arxiv.org/abs/1101.3041v1

Mathematics

Metric Geometry

6 pages, 2 figures

Scientific paper

We consider a class of cut-and-project sets $\Lambda = \Lambda_F \times
\zahl$ in the plane. Let $L=\Lambda+w\real$, $w\in\real^2$, be a countable
union of parallel lines. Then either (1) $L$ is a discrete family of lines, (2)
$L$ is a dense subset of $\real^2$, or (3) each connected component of the
closure of $L$ is homeomorphic to $[0,1] \times \real$.

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