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UNIVERSAL MINIMAL FLOWS OF GENERALIZED WAŻEWSKI DENDRITES

Published online by Cambridge University Press:  21 December 2018

ALEKSANDRA KWIATKOWSKA
ALEKSANDRA KWIATKOWSKA*
Affiliation:
INSTITUT FÜR MATHEMATISCHE LOGIK UND GRUNDLAGENFORSCHUNGUNIVERSITÄT MÜNSTEREINSTEINSTRASSE 62 48149 MÜNSTER, GERMANY and INSTYTUT MATEMATYCZNYUNIWERSYTET WROCŁAWSKIPL. GRUNWALDZKI 2/4 50-384 WROCŁAW, POLANDE-mail: [email protected]
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Abstract

We study universal minimal flows of the homeomorphism groups of generalized Ważewski dendrites WP, $P \subseteq \left\{ {3,4, \ldots ,\omega } \right\}$. If P is finite, we prove that the universal minimal flow of the homeomorphism group H (WP) is metrizable and we compute it explicitly. This answers a question of Duchesne. If P is infinite, we show that the universal minimal flow of H (WP) is not metrizable. This provides examples of topological groups which are Roelcke precompact and have a nonmetrizable universal minimal flow with a comeager orbit.

Keywords

05D1037B0554F1503C98universal minimal flowshomeomorphism groups of Ważewski dendritesFraïssé limits
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 4 , December 2018 , pp. 1618 - 1632
Copyright
Copyright © The Association for Symbolic Logic 2018 

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