The homeomorphism group of the first uncountable ordinal
Maxime Gheysens
Technische Universität Bergakademie Freiberg, Germany
![The homeomorphism group of the first uncountable ordinal cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-lem-volume-67-issue-1.png&w=3840&q=90)
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.
Cite this article
Maxime Gheysens, The homeomorphism group of the first uncountable ordinal. Enseign. Math. 67 (2021), no. 1/2, pp. 145–159
DOI 10.4171/LEM/1006