Dynamics and structure of groups of homeomorphisms of scattered spaces
Group Theory
2020-12-01 v1 General Topology
Abstract
We study the topological structure and the topological dynamics of groups of homeomorphisms of scattered spaces. For a large class of them (including the homeomorphism group of any ordinal space or of any locally compact scattered space), we establish Roelcke-precompactness and amenability, classify all closed normal subgroups and compute the universal minimal flow. As a by-product, we classify up to isomorphism the homeomorphism groups of compact ordinal spaces.
Keywords
Cite
@article{arxiv.2011.15009,
title = {Dynamics and structure of groups of homeomorphisms of scattered spaces},
author = {Maxime Gheysens},
journal= {arXiv preprint arXiv:2011.15009},
year = {2020}
}