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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.

Irresolvable countable spaces of weight less than ℭ

Viacheslav I. Malykhin (1999)

Commentationes Mathematicae Universitatis Carolinae

We construct in Bell-Kunen’s model: (a) a group maximal topology on a countable infinite Boolean group of weight ℵ 1 < ℭ and (b) a countable irresolvable dense subspace of 2 ω 1 . In this model ℭ = ℵ ω 1 .

Isometry groups of non standard metric products

Bogdana Oliynyk (2013)

Open Mathematics

We consider isometry groups of a fairly general class of non standard products of metric spaces. We present sufficient conditions under which the isometry group of a non standard product of metric spaces splits as a permutation group into direct or wreath product of isometry groups of some metric spaces.

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