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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The universal minimal flow of the homeomorphism group of the Lelek fan


Authors: Dana Bartošová and Aleksandra Kwiatkowska
Journal: Trans. Amer. Math. Soc. 371 (2019), 6995-7027
MSC (2010): Primary 05D10, 37B05, 54F15, 03C98
DOI: https://doi.org/10.1090/tran/7548
Published electronically: September 25, 2018
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Abstract: We compute the universal minimal flow of the homeomorphism group of the Lelek fan--a one-dimensional tree-like continuum with many symmetries.


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Additional Information

Dana Bartošová
Affiliation: Institute de Matematica e Estatística, Universidade de São Paulo, Brazil; and Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania
Email: dbartoso@andrew.cmu.edu

Aleksandra Kwiatkowska
Affiliation: Institut für Mathematische Logik und Grundlagenforschung, Universität Münster, Einsteinstrasse 62, 48149 Münster, Germany; and Instytut Matematyczny, Uniwersytet Wrocławski, plac Grunwaldzki 2/4, 50-384 Wrocław, Poland
Email: kwiatkoa@uni-muenster.de

DOI: https://doi.org/10.1090/tran/7548
Keywords: Dual Ramsey theorem, universal minimal flows, homeomorphism group of the Lelek fan, Fra\"{\i}ss\'e limits
Received by editor(s): June 28, 2017
Received by editor(s) in revised form: February 6, 2018
Published electronically: September 25, 2018
Additional Notes: The first author was supported by FAPESP (grant 2013/14458-9) and FAPESP (grant 2014/12405-8).
The second author was supported by Narodowe Centrum Nauki grant 2016/23/D/ST1/01097.
Article copyright: © Copyright 2018 American Mathematical Society