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Invariant metrics on G -spaces

Bogusław Hajduk;  Rafał Walczak — 2003

Czechoslovak Mathematical Journal

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.

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