Fundamental study: Dcpo-completion of posets

Authors:
Dongsheng Zhao;Taihe Fan
Affiliations:
Mathematics and Mathematics Education, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, Singapore;Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, Zhejiang, 310018, China
Venue:
Theoretical Computer Science
Year:
2010

Citing 1
Cited 2

The essence of ideal completion in quantitative form

Theoretical Computer Science

Join-completions of L-ordered sets

Fuzzy Sets and Systems
Applying quantitative semantics to higher-order quantum computing

Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

Quantified Score

Hi-index	5.23

Visualization

Abstract

We introduce a new type of dcpo-completion of posets, called D-completion. For any poset P, the D-completion exists, and P and its D-completion have the isomorphic Scott closed set lattices. This completion is idempotent. A poset P is continuous (algebraic) if and only if its D-completion is continuous(algebraic). Using the D-completion, we construct the local dcpo-completion of posets, that revises the one given by Mislove. In the last section, we define and study bounded sober spaces.