Direct limits of large orbits and the Knaster continuum homeomorphism group

Autor:	Iyer, Sumun
Rok vydání:	2023
Předmět:	Mathematics - Dynamical Systems Mathematics - Logic 03E15 (Primary) 37B05 54F15 (Secondary)
Druh dokumentu:	Working Paper
Popis:	The main result is that the group $\textrm{Homeo} (K)$ of homeomorphisms of the universal Knaster continuum contains an open subgroup with a comeager conjugacy class. Actually, this open subgroup is the very natural subgroup consisting of degree-one homeomorphisms. We give a general fact about finding comeager orbits in Polish group actions which are approximated densely by direct limits of actions with comeager orbits. The main theorem comes as a result of this fact and some finer analysis of the conjugacy action of the group $\textrm{Homeo}_+[0,1]$. Comment: 16 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2308.13023 Zobrazit plný text záznamu View this record from Arxiv