Tilings whose members have finitely many neighbors
type: Item
instance of: scholarly article
title: Tilings whose members have finitely many neighbors
zbMATH Open document ID: 0585.52006
DOI: 10.1007/BF02776087
author: Marilyn Breen
published in: Israel Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: The article studies plane tilings in which each tile meets at most finitely many other tiles. Let S be the set of singular points in a tiling and let W denote the set of boundary points which belong to ''no nondegenerate'' edge of the tiling. It is shown that exactly one of the following must occur: Either W is uncountable and so is S; or both are empty. Furthermore it is proven that the closure of W is exactly S. The inclusion \(S\subseteq cl W\) also holds but in general \(S\varsubsetneq W\), though \(S\supseteq W\) is always true.
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 05B45
zbMATH DE Number: 3937955
zbMATH Keywords: tiling by closed topological discs in the Euclidean plane
reviewed by: Ágota H. Temesvári
MaRDI profile type: Publication
cites work: A characterization theorem for tilings having countably many singular points
cites work: Tilings of the plane by topological disks
description: scientific article; zbMATH DE number 3937955