Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4657945 | Topology and its Applications | 2016 | 4 Pages |
Abstract
In this note, we prove that a well-filtered dcpo L is coherent in its Scott topology if and only if for every x,y∈Lx,y∈L, ↑x∩↑y↑x∩↑y is compact in the Scott topology. We use this result to prove that a well-filtered dcpo L is Lawson-compact if and only if it is patch-compact if and only if L is finitely generated and ↑x∩↑y↑x∩↑y is compact in the Scott topology for every x,y∈Lx,y∈L.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Xiaodong Jia, Achim Jung, Qingguo Li,