All cartesian closed categories of quasicontinuous domains consist of domains

Xiaodong Jia, Achim Jung, Hui Kou, Qingguo Li, Haoran Zhao

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5 Citations (Scopus)
288 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)143-150
Number of pages9
JournalTheoretical Computer Science
Volume594
Early online date21 May 2015
DOIs
Publication statusPublished - 23 Aug 2015

Keywords

  • cartesian closed category
  • quasicontinuous domain
  • meet-continuity
  • meet*-continuity

ASJC Scopus subject areas

  • Theoretical Computer Science

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