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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Some tilings of the plane whose singular points form a perfect set


Author: Marilyn Breen
Journal: Proc. Amer. Math. Soc. 89 (1983), 477-479
MSC: Primary 52A45; Secondary 05B45
MathSciNet review: 715870
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Abstract: Let $ \mathcal{J}$ be a tiling of the plane such that for every tile $ T$ of $ \mathcal{J}$ there correspond a tile $ T'$ of $ \mathcal{J}$ (not necessarily unique) and an integer $ k(T,T')$ (depending on $ T$ and $ T'$), $ 2 < k$, such that $ T$ meets $ T'$ in $ k(T,T')$ connected components. Then the set of singular points of $ \mathcal{J}$ is a nowhere dense, perfect set.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0715870-7
PII: S 0002-9939(1983)0715870-7
Article copyright: © Copyright 1983 American Mathematical Society