Function spaces of Lawson-compact algebraic domains

IF 0.5 4区数学 Q3 MATHEMATICS Topology and its Applications Pub Date : 2025-05-01 Epub Date: 2025-02-25 DOI:10.1016/j.topol.2025.109295

Wei Luan , Qingguo Li

引用次数: 0

Abstract

In this paper, we investigate function spaces of Lawson-compact algebraic domains. It is proved that a dcpo is a Lawson-compact algebraic domain iff there is an approximate identity consisting of Scott-continuous kernel operators whose images are prefinite algebraic domains. Using this fact, we obtain the following results:

(1)
The function space from a bifinite domain to a Lawson-compact algebraic domain is a Lawson-compact algebraic domain.
(2)
An algebraic domain X is bifinite iff $[X \to L]$ is a domain for each domain L.
(3)
The function space from a Lawson-compact algebraic domain to a bifinite domain (not necessarily pointed) is a bifinite domain.

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lawson紧代数域的函数空间

本文研究了lawson -紧代数域上的函数空间。证明了如果存在一个由scott -连续核算子组成的近似恒等式，其象是有限代数域，则dcpo是lawson -紧代数域。利用这一事实，我们得到了以下结果：(1)从双有限域到lawson -紧代数域的函数空间是一个lawson -紧代数域。(2)代数域X是双有限的iff [X→L]是每个域L的一个域。(3)从lawson -紧代数域到双有限域（不一定是点）的函数空间是一个双有限域。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.

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