On well-filtered spaces and ordered sets
On well-filtered spaces and ordered sets
复制标题
在过滤良好的空间和有序集上
DOI：
10.1016/j.topol.2017.06.002
复制
发表时间：
2017
影响因子：
0.6
通讯作者：
Lawson Jimmie
中科院分区：
文献类型：
--
作者：
Xi Xiaoyong;Lawson Jimmie
如果在一个开集中有交的紧集的任何被过滤的族必须有该族的某些成员包含在这个开集中，那么拓扑空间就是被良好过滤的。这一众所周知的重要性质在豪斯多夫空间中自动得到满足，在t0环境中具有自己的生命。我们的主要结果集中在给出t0空间被良好过滤的一般充分条件，特别是具有Scott拓扑的有向完全部分有序集的重要情况。
A topological space is well-filtered if any filtered family of compact sets with intersection in an open set must have some member of the family contained in the open set. This well-known and important property automatically satisfied in Hausdorff spaces assumes a life of its own in the T 0-setting. Our main results focus on giving general sufficient conditions for a T 0-space to be well-filtered, particularly the important case of directed complete partially ordered sets equipped with the Scott topology.