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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 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Dendrites as Polish structures
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by Riccardo Camerlo PDF
Proc. Amer. Math. Soc. 139 (2011), 2217-2225 Request permission

Abstract:

It is shown that standard universal dendrites under the action of their group of homeomorphisms give rise to small Polish structures. Moreover, any non-singleton dendrite forming a small Polish structure (or, more generally, having at least one uncountable orbit) under the action of its group of homeomorphisms has $\mathcal N \mathcal M$-rank $1$. Finally, dendrites satisfy the existence of nm-independent extensions.
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Additional Information
  • Riccardo Camerlo
  • Affiliation: Dipartimento di Matematica, Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Turin, Italy
  • MR Author ID: 663257
  • Email: camerlo@calvino.polito.it
  • Received by editor(s): December 8, 2009
  • Received by editor(s) in revised form: May 5, 2010, June 1, 2010, and June 4, 2010
  • Published electronically: November 10, 2010
  • Communicated by: Julia Knight
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 2217-2225
  • MSC (2010): Primary 03C45, 03E15, 54F15
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10627-5
  • MathSciNet review: 2775399