论文标题
无限尺寸双曲空间的等轴测图的波兰拓扑
The Polish topology of the isometry group of the infinite dimensional hyperbolic space
论文作者
论文摘要
我们认为无限尺寸可分离双曲线空间的等轴测图及其抛光拓扑。该拓扑由点融合给出。对于非局部紧凑的抛光群，可能会发生一些惊人的现象，例如自动连续性或极端的舒适性。我们的主要思想是将这个拓扑组与一侧的通常的谎言组与非架构的无限尺寸组进行比较，例如$ \ Mathcal {s} _ \ infty $，这是另一侧可数集的所有排列的组。我们的主要结果是 自动连续性（对可分离群体的任何同构性是连续的），波兰拓扑结构的最小值，将其通用的furstenberg边界鉴定为可分离的希尔伯特空间的封闭单位球，其较弱的拓扑结构，将其通用的最小流程确定为对真实添加剂在通用最小值流动的悬挂的暂停。 在本文中，我们通过可分离的希尔伯特空间的同学同源群进行了一项平行的研究。
We consider the isometry group of the infinite dimensional separable hyperbolic space with its Polish topology. This topology is given by the pointwise convergence. For non-locally compact Polish groups, some striking phenomena like automatic continuity or extreme amenability may happen. Our leading idea is to compare this topological group with usual Lie groups on one side and with non-Archimedean infinite dimensional groups like $\mathcal{S}_\infty$, the group of all permutations of a countable set on the other side. Our main results are Automatic continuity (any homomorphism to a separable group is continuous), minimality of the Polish topology, identification of its universal Furstenberg boundary as the closed unit ball of a separable Hilbert space with its weak topology, identification of its universal minimal flow as the completion of some suspension of the action of the additive group of the reals on its universal minimal flow. All along the text, we lead a parallel study with the sibling group of isometries of a separable Hilbert space.
