论文标题
Urysohn空间和其他度量结构的最大模棱两可的压实
Maximal equivariant compactification of the Urysohn spaces and other metric structures
论文作者
论文摘要
我们研究等距$ g $空间以及它们何时最大的等效压缩的问题是gromov紧凑型（这意味着它与距离函数到点产生的紧凑型相吻合）。在回答Pestov的问题时，我们表明，Urysohn球体和相关空间是这种情况，但对于Gurarij空间的单位球体而言不是。 我们表明，在其自动形态组的行动下，可分开的分类度量结构$ m $的最大模棱两可的压实可以用超过$ m $的空间$ s_1（m）$ nide，并且特别是可移动的。这提供了对以前和其他示例的统一理解。特别是，Gurarij空间和$ l^p $空间的最大模棱两可的压实是可元的。 我们还证明了EFFROS定理的统一版本，用于Roelcke Prefompact Polish组的等轴测动作。
We study isometric $G$-spaces and the question of when their maximal equivariant compactification is the Gromov compactification (meaning that it coincides with the compactification generated by the distance functions to points). Answering questions of Pestov, we show that this is the case for the Urysohn sphere and related spaces, but not for the unit sphere of the Gurarij space. We show that the maximal equivariant compactification of a separably categorical metric structure $M$ under the action of its automorphism group can be identified with the space $S_1(M)$ of 1-types over $M$, and is in particular metrizable. This provides a unified understanding of the previous and other examples. In particular, the maximal equivariant compactifications of the spheres of the Gurarij space and of the $L^p$ spaces are metrizable. We also prove a uniform version of Effros' Theorem for isometric actions of Roelcke precompact Polish groups.
