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A topological version of the Bergman property
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Christian Rosendal
Published/Copyright:
March 12, 2009
Abstract
A topological group G is defined to have property (OB) if any G-action by isometries on a metric space, which is separately continuous, has bounded orbits. We study this topological analogue of strong uncountable cofinality in the context of Polish groups, where we show it to have several interesting reformulations and consequences. We subsequently apply the results obtained in order to verify property (OB) for a number of groups of isometries and homeomorphism groups of compact metric spaces. We also give a proof that the isometry group of the rational Urysohn metric space of diameter 1 has strong uncountable cofinality.
Received: 2005-09-28
Revised: 2007-09-03
Accepted: 2007-09-18
Published Online: 2009-03-12
Published in Print: 2009-March
© de Gruyter 2009
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Articles in the same Issue
- Homotopy theory of small diagrams over large categories
- A classification of transitive ovoids, spreads, and m-systems of polar spaces
- Frobenius complements of exponent dividing 2m · 9
- Asymptotics of class numbers for progressions and for fundamental discriminants
- A difference characterization of Besov and Triebel-Lizorkin spaces on RD-spaces
- A topological version of the Bergman property
- A unified treatment of certain majorization results on eigenvalues and singular values of matrices
- Finite index subgroups of conjugacy separable groups
- A Bohr-like compactification and summability of Fourier series
