Boundary local connectivity of tiles in \(\mathbb R^2\)
type: Item
instance of: scholarly article
title: Boundary local connectivity of tiles in \(\mathbb R^2\)
zbMATH Open document ID: 1116.54012
author: Jun Luo
published in: Topology and its Applications
publication date: 2007-02-02T00:00:00Z
review text: Let \(C_p(r)\) be the circle with radius \(r>0\) centered at the point \(p\) in the plane, and \(A(p,r,R)\) the open annulus bounded by the two circles \(C_p(r)\) and \(C_p(R)\). In this paper the author shows that a continuum \(M\) in the plane is locally connected if and only if for every open annulus \(A(p,r,R)\) with \(p\in M\), the set \(A(p,r,R)\setminus M\) has at most finitely many components whose closures intersect the two circles \(C_p(r)\) and \(C_p(R)\). With this result, the author shows that the boundary of a connected and locally connected tile in the plane is a Peano continuum.
reviewed by: Jan van Mill
Mathematics Subject Classification ID: 54D05
Mathematics Subject Classification ID: 54F15
zbMATH DE Number: 5121453
zbMATH Keywords: local connectivity
zbMATH Keywords: Tile
MaRDI profile type: Publication
full work available at URL: j.topol.2006.07.013
OpenAlex ID: W2018180751
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DOI: 10.1016/J.TOPOL.2006.07.013
description: scientific article; zbMATH DE number 5121453