论文标题
固定点和Noetherian拓扑
Fixed Points and Noetherian Topologies
论文作者
论文摘要
本文提供了Noetherian最不固定点拓扑的规范结构。尽管通常不是固定点的固定点，但我们证明在一个温和的假设下，人们可以使用拓扑最小的不良序列论点来证明它们是。然后，我们将此固定点定理应用于具有统一证明的已知Noetherian拓扑结构。 在归纳定义的空间（例如有限单词和有限树）的情况下，我们使用固定点定理提供了均匀的分裂性拓扑定义。然后，我们证明，在良好的Quasi-orders的情况下，划分性拓扑是对谷川提出的划分性预订的概括。
This paper provides a canonical construction of a Noetherian least fixed point topology. While such least fixed point are not Noetherian in general, we prove that under a mild assumption, one can use a topological minimal bad sequence argument to prove that they are. We then apply this fixed point theorem to rebuild known Noetherian topologies with a uniform proof. In the case of spaces that are defined inductively (such as finite words and finite trees), we provide a uniform definition of a divisibility topology using our fixed point theorem. We then prove that the divisibility topology is a generalisation of the divisibility preorder introduced by Hasegawa in the case of well-quasi-orders.
