All cartesian closed categories of quasicontinuous domains consist of domains

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All cartesian closed categories of quasicontinuous domains consist of domains. / Jia, Xiaodong; Jung, Achim; Kou, Hui; Li, Qingguo; Zhao, Haoran.

In: Theoretical Computer Science, Vol. 594, 23.08.2015, p. 143-150.

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Jia, Xiaodong ; Jung, Achim ; Kou, Hui ; Li, Qingguo ; Zhao, Haoran. / All cartesian closed categories of quasicontinuous domains consist of domains. In: Theoretical Computer Science. 2015 ; Vol. 594. pp. 143-150.

Bibtex

@article{295e3e6b95ff49a5ab0c0dd009dd6c18,
title = "All cartesian closed categories of quasicontinuous domains consist of domains",
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.",
keywords = "cartesian closed category, quasicontinuous domain, meet-continuity, meet*-continuity",
author = "Xiaodong Jia and Achim Jung and Hui Kou and Qingguo Li and Haoran Zhao",
year = "2015",
month = aug,
day = "23",
doi = "10.1016/j.tcs.2015.05.014",
language = "English",
volume = "594",
pages = "143--150",
journal = "Theoretical Computer Science",
issn = "0304-3975",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - All cartesian closed categories of quasicontinuous domains consist of domains

AU - Jia, Xiaodong

AU - Jung, Achim

AU - Kou, Hui

AU - Li, Qingguo

AU - Zhao, Haoran

PY - 2015/8/23

Y1 - 2015/8/23

N2 - 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.

AB - 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.

KW - cartesian closed category

KW - quasicontinuous domain

KW - meet-continuity

KW - meet-continuity

U2 - 10.1016/j.tcs.2015.05.014

DO - 10.1016/j.tcs.2015.05.014

M3 - Article

VL - 594

SP - 143

EP - 150

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -