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Homogeneous spaces and transitive actions by Polish groups

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Abstract

We prove that for every homogeneous and strongly locally homogeneous Polish space X there is a Polish group admitting a transitive action on X. We also construct an example of a homogeneous Polish space which is not a coset space and on which no separable metrizable topological group acts transitively.

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  1. Faculty of Sciences, Department of Mathematics, Vrije Universiteit, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    Jan van Mill

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van Mill, J. Homogeneous spaces and transitive actions by Polish groups. Isr. J. Math. 165, 133–159 (2008). https://doi.org/10.1007/s11856-008-1007-0

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  • DOI: https://doi.org/10.1007/s11856-008-1007-0

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