# Proper actions and proper invariant metrics

Abels H, Manoussos A, Noskov G (2011)
Journal of the London Mathematical Society 83(3): 619-636.

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Journal Article | Published | English

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We show that if a (locally compact) group $G$ acts properly on a locallycompact $\sigma$-compact space $X$ then there is a family of $G$-invariantproper continuous finite-valued pseudometrics which induces the topology of$X$. If $X$ is furthermore metrizable then $G$ acts properly on $X$ if and onlyif there exists a $G$-invariant proper compatible metric on $X$.
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Abels H, Manoussos A, Noskov G. Proper actions and proper invariant metrics. Journal of the London Mathematical Society. 2011;83(3):619-636.
Abels, H., Manoussos, A., & Noskov, G. (2011). Proper actions and proper invariant metrics. Journal of the London Mathematical Society, 83(3), 619-636. doi:10.1112/jlms/jdq091
Abels, H., Manoussos, A., and Noskov, G. (2011). Proper actions and proper invariant metrics. Journal of the London Mathematical Society 83, 619-636.
Abels, H., Manoussos, A., & Noskov, G., 2011. Proper actions and proper invariant metrics. Journal of the London Mathematical Society, 83(3), p 619-636.
H. Abels, A. Manoussos, and G. Noskov, “Proper actions and proper invariant metrics”, Journal of the London Mathematical Society, vol. 83, 2011, pp. 619-636.
Abels, H., Manoussos, A., Noskov, G.: Proper actions and proper invariant metrics. Journal of the London Mathematical Society. 83, 619-636 (2011).
Abels, Herbert, Manoussos, Antonios, and Noskov, Gennady. “Proper actions and proper invariant metrics”. Journal of the London Mathematical Society 83.3 (2011): 619-636.
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arXiv math/0702322