Homogeneous Spaces and Transitive Actions by Polish Groups
نویسنده
چکیده
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.
منابع مشابه
Topology Proceedings 33 (2009) pp. 153-161: Homogeneous spaces and transitive actions by $\aleph_0$-bounded groups
We construct a homogeneous connected Polish space X on which no א0-bounded topological group acts transitively. In fact, X is homeomorphic to a convex subset of Hilbert space `.
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