论文标题
局部界限统一的空间和拓扑组的自动形态
Uniformly locally bounded spaces and the group of automorphisms of a topological group
论文作者
论文摘要
我们表明，有限集对统一的融合的拓扑结构与既有均匀结构又有天生学的大型空间的自动形态群体的群体定律兼容，从而产生了许多拓扑组的例子。这包括许多先前已知的病例，例如局部紧凑空间的同构群，一阶结构的自动形态群，常规空间的一般线性群体，统一空间的自动形态群体等。我们还研究了该框架内拓扑组的自动形态群体（在局部紧凑型组中概括了先前已知的拓扑组）。作为这种机械的特殊结果，我们表明，波兰本地roelcke-ecompact群体的自动形态群体具有自然的波兰群体拓扑。
We show that the topology of uniform convergence on bounded sets is compatible with the group law of the automorphism group of a large class of spaces that are endowed with both a uniform structure and a bornology, thus yielding numerous examples of topological groups. This encompasses many of previously known cases, such as homeomorphism groups of locally compact spaces, automorphism groups of first-order structures, general linear groups of normed spaces, automorphism groups of uniform spaces, etc. We also study the automorphism group of a topological group within this framework (generalizing previously known results on locally compact groups). As a particular outcome of this machinery, we show that the automorphism group of a Polish locally Roelcke-precompact group carries a natural Polish group topology.
