论文标题
关于关系结构的内态性质的波兰拓扑
Polish topologies on endomorphism monoids of relational structures
论文作者
论文摘要
在本文中，我们介绍了表征内态和最大半群拓扑的一般技术。作为应用，我们表明几种众所周知的关系结构的内态单体，包括随机图，随机图形和随机部分阶，具有独特的波兰半群拓扑。在每种情况下，这种独特的拓扑都是Baire Space $ \ Mathbb {n} ^ \ Mathbb {n} $引起的子空间拓扑。我们还表明，这些结构中的许多同态从它们的内态单态到第二个可计数的拓扑半群都是连续的。称为自动连续性。关于内态性单体的许多结果扩展到相同结构上的多态性克隆。
In this paper we present general techniques for characterising minimal and maximal semigroup topologies on the endomorphism monoid $\operatorname{End}(\mathbb{A})$ of a countable relational structure $\mathbb{A}$. As applications, we show that the endomorphism monoids of several well-known relational structures, including the random graph, the random directed graph, and the random partial order, possess a unique Polish semigroup topology. In every case this unique topology is the subspace topology induced by the usual topology on the Baire space $\mathbb{N} ^ \mathbb{N}$. We also show that many of these structures have the property that every homomorphism from their endomorphism monoid to a second countable topological semigroup is continuous; referred to as automatic continuity. Many of the results about endomorphism monoids are extended to clones of polymorphisms on the same structures.
