Universal minimal flows of generalized Wa\.zewski dendrites

Autor:	Kwiatkowska, Aleksandra
Rok vydání:	2017
Předmět:	Mathematics - Logic Mathematics - Combinatorics Mathematics - Dynamical Systems
Zdroj:	J. symb. log. 83 (2018) 1618-1632
Druh dokumentu:	Working Paper
DOI:	10.1017/jsl.2018.26
Popis:	We study universal minimal flows of the homeomorphism groups of generalized Wa\.zewski dendrites $W_P$, $P\subset\{3,4,\ldots,\omega\}$. If $P$ is finite, we prove that the universal minimal flow of of the homeomorphism group $H(W_P)$ is metrizable and we compute it explicitly. This answers a question of B. Duchesne. If $P$ is infinite, we show that the universal minimal flow of $H(W_P)$ is not metrizable. This provides examples of topological groups which are Roelcke precompact and have a non-metrizable universal minimal flow with a comeager orbit. Comment: final version, accepted to the Journal of Symbolic Logic
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1711.07869 Zobrazit plný text záznamu View this record from Arxiv