The homeomorphism group of the first uncountable ordinal

2019/11/20 by Maxime Gheysens, Gheysens, Maxime
Mathematics · #43A07 #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR) #Primary 20F38 #Secondary 54G12 #math.GN #math.GR #msc:20F38 #msc:43A07 #msc:54G12

paper · pdf · doi:10.48550/arxiv.1911.09088

Second version: various additions to make a bridge with results of the companion paper arXiv:2011.15009 (new paragraph at the end of the introduction, new Remark 11, new paragraphs in Remarks 18 and 20). Also, new Footnote 2 and new Remark 19. Some results have different labelling or shifted numbering in comparison to the first version

arxiv created 2020/12/01 · arxiv updated 2020/12/02

Abstract

We show that the topology of pointwise convergence on scattered spaces is compatible with the group structure of their homeomorphism group. We then establish a few topological properties of the homeomorphism group of the first uncountable ordinal, such as amenability and Roelcke-precompactness.

Citations

• Dynamics and structure of groups of homeomorphisms of scattered spaces

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