Isometrisable group actions
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- by Itaï Ben Yaacov and Julien Melleray
- Proc. Amer. Math. Soc. 144 (2016), 4081-4088
- DOI: https://doi.org/10.1090/proc/13018
- Published electronically: February 17, 2016
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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.References
- Carlos R. Borges, How to recognize homeomorphisms and isometries, Pacific J. Math. 37 (1971), 625–633. MR 305328, DOI 10.2140/pjm.1971.37.625
- Ryszard Engelking, General topology, 2nd ed., Sigma Series in Pure Mathematics, vol. 6, Heldermann Verlag, Berlin, 1989. Translated from the Polish by the author. MR 1039321
- Mo Tak Kiang, On some semigroups of mappings, Indag. Math. 35 (1973), 18–22. Nederl. Akad. Wetensch. Proc. Ser. A 76. MR 0317287, DOI 10.1016/1385-7258(73)90016-4
- M. M. Marjanović, On topological isometries, Indag. Math. 31 (1969), 184–189. Nederl. Akad. Wetensch. Proc. Ser. A 72. MR 0246252, DOI 10.1016/1385-7258(69)90008-0
- H. L. Royden, Real analysis, 3rd ed., Macmillan Publishing Company, New York, 1988. MR 1013117
Bibliographic 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