Homogeneous spaces and transitive actions by Polish groups

J. van Mill

doi:10.1007/s11856-008-1007-0

Homogeneous spaces and transitive actions by Polish groups

J. van Mill

Mathematics

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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. © 2008 The Hebrew University of Jerusalem.

Original language	English
Pages (from-to)	133-159
Journal	Israel Journal of Mathematics
Volume	165
DOIs	https://doi.org/10.1007/s11856-008-1007-0
Publication status	Published - 2008

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MR2403618

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10.1007/s11856-008-1007-0

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AB - 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. © 2008 The Hebrew University of Jerusalem.

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JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

ER -

Homogeneous spaces and transitive actions by Polish groups

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