作为 Lévy 群的 Urysohn 空间等距群
一般拓扑
2007-09-03 v3
摘要
我们证明配备自然 Polish 拓扑的泛 Urysohn 度量空间 的等距群 是 Gromov 与 Milman 意义下的 L\'evy 群，即容许一列紧（实为有限）子群的逼近链，并呈现测度集中现象。这加强了 Vershik 早先关于 具有稠密局部有限子群的结果。
关键词
引用
@article{arxiv.math/0509402,
title = {The isometry group of the Urysohn space as a Levy group},
author = {Vladimir Pestov},
journal= {arXiv preprint arXiv:math/0509402},
year = {2007}
}
备注
20 pages, LaTeX 2e with Elsevier macros, final version, to appear in Proc. 6-th Iberoamerican Conf. on Topology and its Applications (Puebla, Mexico, 4-7 July 2005). Section 3 is removed to become a part of a joint paper with V.V. Uspenskij ``Representations of residually finite groups by isometries of the Urysohn space'' (math.RT/0601700)