The Injective Hull and the -Compactification of a Continuous Poset

Author:

Hoffmann Rudolf-E.

Abstract

In [57] (2.12), D. S. Scott showed that the continuous lattices, invented by him in his study of a mathematical theory of computation [56], are precisely (when they are made into topological spaces via the Scott topology) the injective T0-spaces, i.e., the injective objects in the category T0 of T0-spaces and continuous maps with regard to the class of all embeddings. Moreover, the sort of morphisms between continuous lattices Scott considered are precisely the continuous maps with regard to the respective Scott topologies. These are fairly non-Hausdorff topologies. (Indeed, the Scott topology induces the partial order of the lattice L via xy if and only if x ∊ cl{j}, the “specialization order” of the topology; hence L is Hausdorff in the Scott topology if and only if L has at most one element.) In topological algebra, compact Lawson semilattices (= compact Hausdorff topological ∧-semilattices such that the ∧-preserving continuous maps into the unit interval, with its ordinary topology and the min-semilattice structure, separate the points) with a unit element 1 have attracted considerable interest.

Publisher

Canadian Mathematical Society

Subject

General Mathematics

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Transporting continuity properties from a poset to its subposets;Theoretical Computer Science;2022-04

2. Injective Hulls of Quantale-Enriched Multicategories;Applied Categorical Structures;2021-06-20

3. Equational theory of continuous lattices;Semigroup Forum;1991-12

4. A continuous latticeL withDID (L) incomplete;Semigroup Forum;1986-12

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3