On sobriety of Scott topology on dcpos
Xiaoquan Xu
TL;DR
This paper investigates the conditions for the Scott topology on product dcpos to be equal to the product of their Scott topologies and explores when the Scott topology on a dcpo is sober, providing specific criteria.
Contribution
It offers new conditions under which the Scott topology on product dcpos matches the product topology and characterizes when the Scott topology on a dcpo is sober.
Findings
Identifies conditions for Scott topology equality on product dcpos.
Provides criteria for sobriety of Scott topology on dcpos.
Advances understanding of Scott topology properties in domain theory.
Abstract
In this paper, we mainly investigate the conditions under which the Scott topology on the product of two posets is equal to the product of the individual Scott topologies and under which the Scott topology on a dcpo is sober. Some such conditions are given.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Rings, Modules, and Algebras · Advanced Topology and Set Theory