Displaying similar documents to “A reconstruction theorem for locally moving groups acting on completely metrizable spaces”

Proper actions of locally compact groups on equivariant absolute extensors

Sergey Antonyan (2009)

Fundamenta Mathematicae

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Let G be a locally compact Hausdorff group. We study equivariant absolute (neighborhood) extensors (G-AE's and G-ANE's) in the category G-ℳ of all proper G-spaces that are metrizable by a G-invariant metric. We first solve the linearization problem for proper group actions by proving that each X ∈ G-ℳ admits an equivariant embedding in a Banach G-space L such that L∖{0} is a proper G-space and L∖{0} ∈ G-AE. This implies that in G-ℳ the notions of G-A(N)E and G-A(N)R coincide. Our embedding...

Invariant metrics on G -spaces

Bogusław Hajduk, Rafał Walczak (2003)

Czechoslovak Mathematical Journal

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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.

Non-locally compact Polish groups and two-sided translates of open sets

Maciej Malicki (2008)

Fundamenta Mathematicae

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This paper is devoted to the following question. Suppose that a Polish group G has the property that some non-empty open subset U is covered by finitely many two-sided translates of every other non-empty open subset of G. Is then G necessarily locally compact? Polish groups which do not have the above property are called strongly non-locally compact. We characterize strongly non-locally compact Polish subgroups of S ∞ in terms of group actions, and prove that certain natural classes of...