Some universal constructions in abstract topological dynamics
Some universal constructions in abstract topological dynamics
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抽象拓扑动力学中的一些普遍结构
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发表时间：
1997
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通讯作者：
V. Pestov
中科院分区：
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作者：
V. Pestov
这个小调查的基本普遍建设有关的行动，拓扑群对aparta是围绕一个新的结果-一个内在的描述非常顺从的拓扑群（即，在他们所作用的每一个紧中都有一个固定点），解决了Granirer在1967年提出的一个问题。另一个老问题，其解决方案（在消极的）是注意到这里，是一个1957年猜想Teleman对不可约表示一般拓扑群。我们的论述涵盖了最大的境界和普遍的最小流，以及密切相关的建设和结果，从表示论。我们目前在一个简化的方式非常顺从的群体的已知的例子，并讨论他们的关系与1969年的问题埃利斯。开放性问题，包括那些从边缘学科，审查沿着。
This small survey of basic universal constructions related to the actions of topological groups on compacta is centred around a new result --- an intrinsic description of extremely amenable topological groups (i.e., those having a fixed point in each compactum they act upon), solving a 1967 problem by Granirer. Another old problem whose solution (in the negative) is noted here, is a 1957 conjecture by Teleman on irreducible representations of general topological groups. Our exposition covers the greatest ambit and the universal minimal flow, as well as closely related constructions and results from representation theory. We present in a simplified fashion the known examples of extremely amenable groups and discuss their relationship with a 1969 problem by Ellis. Open questions, including those from bordering disciplines, are reviewed along the way.