Invariant metrics on G-spaces

Boguslaw Hajduk; Rafal Walczak

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Invariant metrics on G-spaces

Boguslaw Hajduk·Rafal Walczak

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Abstract

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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Boguslaw Hajduk, Rafal Walczak. 2001-05-28. Invariant metrics on G-spaces. https://arxiv.org/abs/math/0105230

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