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A reconstruction theorem for locally moving groups acting on completely metrizable spaces

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Ben-Ami E.

Fundamenta Mathematicae

2010

tom 209

nr 1

1-8

Let G be a group which acts by homeomorphisms on a metric space X. We say the action of G is locally moving on X if for every open U ⊆ X there is a g ∈ G such that g↾X ≠ Id while g↾(X∖U) = Id. We prove the following theorem: Theorem A. Let X,Y be completely metrizable spaces and let G be a group which acts on X and Y with locally moving actions. If the orbits of the action of G on X are of the second category in X and the orbits of the action of G on Y are of the second category in Y, then X and Y are homeomorphic. A particular case of Theorem A gives a positive answer to a question of M. Rubin and J. van Mill who asked whether X and Y are homeomorphic whenever G is strongly locally homogeneous on X and Y.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Ben-Ami E.

1 2010

Wyniki wyszukiwania

A reconstruction theorem for locally moving groups acting on completely metrizable spaces