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Isometrisable group actions


Authors: Itaï Ben Yaacov and Julien Melleray
Journal: Proc. Amer. Math. Soc. 144 (2016), 4081-4088
MSC (2010): Primary 22F05, 37B05
Published electronically: February 17, 2016
MathSciNet review: 3513563
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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.


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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

Julien Melleray
Affiliation: Institut Camille Jordan, CNRS UMR 5208, Université Claude Bernard – Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France

DOI: https://doi.org/10.1090/proc/13018
Keywords: Group action, isometric group action, topological space, metric space
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
Article copyright: © Copyright 2016 American Mathematical Society