Homogeneous spaces and transitive actions by Polish groups
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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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- M. Bestvina, Characterizing k-dimensional universal Menger compacta, Memoirs of the American Mathematical Society 71 (1988), no. 380, vi+110.Google Scholar
- E. Glasner and M. Megrelishvili, Some new algebras of functions on toopological groups arising from G-spaces, 2006, preprint.Google Scholar
- M. G. Megrelishvili, Compactification and factorization in the category of G-spaces, in Categorical Topology and its Relation to Analysis, Algebra and Combinatorics (Prague, 1988), World Sci. Publishing, Teaneck, NJ, 1989, pp. 220–237.Google Scholar
- S. Solecki, Polish group topologies, in Sets and proofs, London Math. Soc. Lecture Note Series, vol. 258 (S. B. Cooper and J. K. Truss, eds.), Cambridge University Press, Cambridge, 1999, pp. 339–364.Google Scholar
- V. V. Uspenskii, Why compact groups are dyadic, in General Topology and its Relations to Modern Analysis and Algebra, VI (Prague, 1986), Research and Exposition in Mathematics, vol. 16, Heldermann, Berlin, 1988, pp. 601–610.Google Scholar
- V. V. Uspenskii, Topological groups and Dugundji compact spaces, Matematicheskii Sbornik 180 (1989), 1092–1118.Google Scholar
- J. de Vries, Linearization, compactification and the existence of non-trivial compact extensors for topological transformation groups, in Topology and Measure III, Ernst-Moritz-Arndt-Universität zu Greifswald, 1982, pp. 339–346.Google Scholar