Bergman性质的拓扑形式
A topological version of the Bergman property
摘要：
定义一个拓扑群G具有性质（OB），如果在分离连续的度量空间上的任意G-等距作用都有有界轨道.我们研究这种拓扑类似的所谓的伯格曼属性的背景下，波兰的群体，在那里我们表明它有几个有趣的重新制定和后果。随后，我们应用所获得的结果，以验证性质（OB）的一些群体的同构和同胚群的紧度量空间。证明了直径为1的有理Urysohn度量空间的等距群是Bergman的。
英文摘要：
A topological group G is defined to have property (OB) if any G-action by isometries on a metric space, which is separately continuous, has bounded orbits. We study this topological analogue of the socalled Bergman property in the context of Polish groups, where we show it to have several interesting reformulations and consequences. We subsequently apply the results obtained in order to verify property (OB) for a number of groups of isometries and homeomorphism groups of compact metric spaces. We also give a proof that the isometry group of the rational Urysohn metric space of diameter 1 is Bergman.
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