Mathematical Sciences: Faculty Publications
Topological Properties of a Class of Self-Affine Tiles in R3
Document Type
Article
Publication Date
2-2018
Publication Title
Transactions of the American Mathematical Society
DOI
10.1090/tran/7055
ISSN
1088-6850
Abstract
We construct a class of connected self-affine tiles in R3 and prove that it contains a subclass of tiles that are homeomorphic to a unit ball in R3. Our construction is obtained by generalizing a two-dimensional one by Deng and Lau. The proof of ball-likeness is inspired by the construction of a homeomorphism from Alexander's horned ball to a 3-ball.
Recommended Citation
Deng, Guotai, Chuntai Liu, Sze-Man Ngai.
2018.
"Topological Properties of a Class of Self-Affine Tiles in R3."
Transactions of the American Mathematical Society, 370 (2): 1321-1350.
doi: 10.1090/tran/7055
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/650
Copyright
This work is archived and distributed under the repository's Standard Copyright and Reuse License (opens in new tab). End users may copy, store, and distribute this work without restriction. For all other uses, permission must be obtained from the copyright owners or their authorized agents.
