Isometry groups of separable metric spaces
2009 ◽
Vol 146
(1)
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pp. 67-81
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AbstractWe show that every locally compact Polish group is isomorphic to the isometry group of a proper separable metric space. This answers a question of Gao and Kechris. We also analyze the natural action of the isometry group of a separable ultrametric space on the space. This leads us to a structure theorem representing an arbitrary separable ultrametric space as a bundle with an ultrametric base and with ultrahomogeneous fibers which are invariant under the action of the isometry group.
1972 ◽
Vol 24
(4)
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pp. 622-630
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2017 ◽
Vol 5
(1)
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pp. 138-151
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2010 ◽
Vol 02
(04)
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pp. 581-597
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2013 ◽
Vol 56
(3)
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pp. 519-535
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2011 ◽
Vol 48
(2)
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pp. 145-159
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2013 ◽
Vol 65
(1)
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pp. 222-240
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