The boundaries of self-similar tiles in \(\mathbb{R}^n\)
type: Item
instance of: scholarly article
title: The boundaries of self-similar tiles in \(\mathbb{R}^n\)
zbMATH Open document ID: 0986.28012
DOI: 10.1016/S0166-8641(98)00031-5
published in: Topology and its Applications
publication date: 1999-12-02T00:00:00Z
review text: This paper is devoted to the Hausdorff dimension of the topological boundary of a self-similar set \(K\subseteq \mathbb{R}^n\). The author shows that the Hausdorff dimension of \(K\) must be less than \(n\). Moreover, he gives examples showing that the Hausdorff dimension of the topological boundary of \(K\) can be arbitrarily close to \(n\). He also considers more general self-similar sets in a complete metric space.
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 28A78
Mathematics Subject Classification ID: 52C22
zbMATH DE Number: 1317231
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: topological boundary
zbMATH Keywords: self-similar sets
author: J. Keesling
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: s0166-8641(98)00031-5
OpenAlex ID: W2025746983
Recommended article: On the boundaries of self-similar tiles in $\mathbb {R}^1$
Recommended article: Hausdorff dimension of boundaries of self-affine tiles in \(\mathbb{R}^N\)
Recommended article: The Hausdorff Dimension of the Boundary of a Self-Similar Tile
Recommended article: Boundaries of disk-like self-affine tiles
Recommended article: Self-affine tiles in \(\mathbb{R}^n\)
Recommended article: On self-affine tiles whose boundary is a sphere
Recommended article: Outer Boundaries of Self-Similar Tiles
Recommended article: Equivalence of self-similar and pseudo-self-similar tiling spaces in \(\mathbb R^{2}\)
Recommended article: Boundary parametrization of self-affine tiles
Recommended article: Topology of connected self-similar tiles in the plane with disconnected interiors
description: scientific article; zbMATH DE number 1317231