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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Dendrites as Polish structures


Author: Riccardo Camerlo
Journal: Proc. Amer. Math. Soc. 139 (2011), 2217-2225
MSC (2010): Primary 03C45, 03E15, 54F15
Published electronically: November 10, 2010
MathSciNet review: 2775399
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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
Email: camerlo@calvino.polito.it

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10627-5
PII: S 0002-9939(2010)10627-5
Keywords: Small Polish structure, dendrite, universal dendrite
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.