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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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When the weak separation condition implies the generalized finite type condition
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by Kathryn E. Hare, Kevin G. Hare and Alex Rutar
Proc. Amer. Math. Soc. 149 (2021), 1555-1568
DOI: https://doi.org/10.1090/proc/15307
Published electronically: February 4, 2021

Abstract:

We prove that an iterated function system of similarities on $\mathbb {R}$ that satisfies the weak separation condition and has an interval as its self-similar set is of generalized finite type. It is unknown if the assumption that the self-similar set is an interval is necessary.
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Bibliographic Information
  • Kathryn E. Hare
  • Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, N2L 3G1 Canada
  • MR Author ID: 246969
  • Email: kehare@uwaterloo.ca
  • Kevin G. Hare
  • Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, N2L 3G1 Canada
  • MR Author ID: 690847
  • Email: kghare@uwaterloo.ca
  • Alex Rutar
  • Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, N2L 3G1 Canada
  • Address at time of publication: Mathematical Institute, North Haugh, St Andrews, Fife KY16 9SS, Scotland
  • ORCID: 0000-0001-5173-992X
  • Email: arutar@uwaterloo.ca
  • Received by editor(s): March 17, 2020
  • Received by editor(s) in revised form: August 5, 2020
  • Published electronically: February 4, 2021
  • Additional Notes: The first author was supported by NSERC Grant 2016-03719. The second author was supported by NSERC Grant 2019-03930. The third author was supported by both these grants and the University of Waterloo.
  • Communicated by: Javad Mashreghi
  • © Copyright 2021 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 1555-1568
  • MSC (2020): Primary 28A80
  • DOI: https://doi.org/10.1090/proc/15307
  • MathSciNet review: 4242311