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

• Autorzy: Edmund Ben-Ami
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 22F05: General theory of group and pseudogroup actions
• 54E50: Complete metric spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 209
• Numer: 1
• Strony: 1-8

Daty

wydano

2010

Twórcy

autor

Edmund Ben-Ami

• Department of Mathematics, Ben Gurion University of the Negev, Beer Sheva, Israel

Identyfikatory

DOI

10.4064/fm209-1-1