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Selected Works of Sze-Man Ngai
Article
Topological Properties of a Class of Self-Affine Tiles in R3
Transactions of the American Mathematical Society
  • Guotai Deng, Central China Normal University
  • Chuntai Liu, Wuhan Polytechnic University
  • Sze-Man Ngai, Georgia Southern University
Link
Document Type
Article
Publication Date
2-1-2018
DOI
10.1090/tran/7055
Disciplines
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.

Citation Information
Guotai Deng, Chuntai Liu and Sze-Man Ngai. "Topological Properties of a Class of Self-Affine Tiles in R3" Transactions of the American Mathematical Society Vol. 370 Iss. 2 (2018) p. 1321 - 1350 ISSN: 1088-6850
Available at: http://works.bepress.com/sze-man_ngai/86/