All cartesian closed categories of quasicontinuous domains consist of domains
Research output: Contribution to journal › Article › peer-review
Authors
Colleges, School and Institutes
External organisations
- Sichuan University
- Hunan University of Humanities, Science and Technology
Abstract
Quasicontinuity is a generalisation of Scott's notion of continuous domain, introduced in the early 80s by Gierz, Lawson and Stralka. In this paper we ask which cartesian closed full subcategories exist in qCONT, the category of all quasicontinuous domains and Scott-continuous functions. The surprising, and perhaps disappointing, answer turns out to be that all such subcategories consist entirely of continuous domains. In other words, there are no new cartesian closed full subcategories in qCONT beyond those already known to exist in CONT.
To prove this, we reduce the notion of meet-continuity for dcpos to one which only involves well-ordered chains. This allows us to characterise meet-continuity by “forbidden substructures”. We then show that each forbidden substructure has a non-quasicontinuous function space.
To prove this, we reduce the notion of meet-continuity for dcpos to one which only involves well-ordered chains. This allows us to characterise meet-continuity by “forbidden substructures”. We then show that each forbidden substructure has a non-quasicontinuous function space.
Details
| Original language | English |
|---|---|
| Pages (from-to) | 143-150 |
| Number of pages | 9 |
| Journal | Theoretical Computer Science |
| Volume | 594 |
| Early online date | 21 May 2015 |
| Publication status | Published - 23 Aug 2015 |
Keywords
- cartesian closed category, quasicontinuous domain, meet-continuity, meet*-continuity