All cartesian closed categories of quasicontinuous domains consist of domains

被引：10

作者：

Jia, Xiaodong ^{[1
,2
]}

Jung, Achim ^{[2
]}

Kou, Hui ^{[3
]}

Li, Qingguo ^{[1
]}

Zhao, Haoran ^{[3
]}

机构：

[1] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China

[2] Univ Birmingham, Sch Comp Sci, Birmingham B15 2TT, W Midlands, England

[3] Sichuan Univ, Coll Math, Chengdu 610064, Peoples R China

来源：

THEORETICAL COMPUTER SCIENCE | 2015年 / 594卷

基金：

中国国家自然科学基金; 高等学校博士学科点专项科研基金;

关键词：

Cartesian closed category; Quasicontinuous domain; Meet-continuity; Meet*-continuity;

D O I：

10.1016/j.tcs.2015.05.014

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

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. Crown Copyright (C) 2015 Published by Elsevier B.V. All rights reserved.

引用

页码：143 / 150

页数：8

共 19 条

[1]

Abramsky S., 1994, Handbook of Logic in Computer Science: Semantic Structures, V3, P1, DOI DOI 10.1093/OSO/9780198537625.003.0001

[2]

[Anonymous], 1990, Ph.D. Dissertation

[3]

[Anonymous], 1944, Zenkoku Shijo Sugaku Danwakai

[4]

GIERZ G, 1983, HOUSTON J MATH, V9, P191

[5]

Gierz G., 2003, Continuous Lattices and Domains

[6]

Goubault-Larrecq J., 2012, LOG METHODS COMPUT S, V8

[7]

Goubault-Larrecq J, 2014, ELECTRON NOTES THEOR, V308, P167, DOI 10.1016/j.entcs.2014.10.010

[8] Quasicontinuous Domains and the Smyth Powerdomain [J].

Heckmann, Reinhold ;

Keimel, Klaus .

ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE, 2013, 298 :215-232

[9]

Jones C., 1989, Proceedings. Fourth Annual Symposium on Logic in Computer Science (Cat. No.89CH2753-2), P186, DOI 10.1109/LICS.1989.39173

[10]

Jung A., 1990, Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science (90CH2897-7), P35, DOI 10.1109/LICS.1990.113731

← 1 2 →