Isometrisable group actions
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- by Itaï Ben Yaacov and Julien Melleray PDF
- Proc. Amer. Math. Soc. 144 (2016), 4081-4088 Request permission
Abstract:
Given a separable metrisable space $X$, and a group $G$ of homeomorphisms of $X$, we introduce a topological property of the action $G \curvearrowright X$ which is equivalent to the existence of a $G$-invariant compatible metric on $X$. This extends a result of Marjanović obtained under the additional assumption that $X$ is locally compact.References
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Additional Information
- Itaï Ben Yaacov
- Affiliation: Institut Camille Jordan, CNRS UMR 5208, Université Claude Bernard – Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France
- MR Author ID: 699648
- Julien Melleray
- Affiliation: Institut Camille Jordan, CNRS UMR 5208, Université Claude Bernard – Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France
- MR Author ID: 781936
- Received by editor(s): June 30, 2014
- Received by editor(s) in revised form: October 28, 2015
- Published electronically: February 17, 2016
- Additional Notes: This research was supported by ANR project GruPoLoCo (ANR-11-JS01-008).
- Communicated by: Kevin Whyte
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 4081-4088
- MSC (2010): Primary 22F05, 37B05
- DOI: https://doi.org/10.1090/proc/13018
- MathSciNet review: 3513563