Geodesic
Invariant metrics on $G$-spaces
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 2, pp. 449-466
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Let $X$ be a $G$-space such that the orbit space $X/G$ is metrizable. Suppose a family of slices is given at each point of $X$. We study a construction which associates, under some conditions on the family of slices, with any metric on $X/G$ an invariant metric on $X$. We show also that a family of slices with the required properties exists for any action of a countable group on a locally compact and locally connected metric space.
Let $X$ be a $G$-space such that the orbit space $X/G$ is metrizable. Suppose a family of slices is given at each point of $X$. We study a construction which associates, under some conditions on the family of slices, with any metric on $X/G$ an invariant metric on $X$. We show also that a family of slices with the required properties exists for any action of a countable group on a locally compact and locally connected metric space.
Classification : 54E35, 54H15, 57S30
Keywords: G-space; invariant metric; slice 
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     title = {Invariant metrics on $G$-spaces},
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}
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Hajduk, Bogusław; Walczak, Rafał. Invariant metrics on $G$-spaces. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 2, pp. 449-466. http://geodesic.mathdoc.fr/item/CMJ_2003_53_2_a18/

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