拟度量空间的局部Yoneda补全

IF 0.4 4区 计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS Mathematical Structures in Computer Science Pub Date : 2023-01-01 DOI:10.1017/S0960129523000105
Jing Lu, Bin Zhao
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引用次数: 0

摘要

摘要本文利用域理论研究了拟度量空间。给定一个拟度量空间(X,d),我们使用$({\bf B}(X,d),\leq^{d^{+}!)$表示相关的拟度量空间(X,d)的形式球的偏序集。根据$({\bf B}(X,d),\leq^{d^{+}}!)$的域理论性质,我们引入了局部Yoneda完备拟度量空间的概念。这个定义的获得方式受到了Romaguera–Valero定理和Kostanek–Waszkiewicz定理的启发。此外,我们通过拟度量空间中的局部网得到了局部Yoneda完备拟度量空间的特征。更确切地说,我们证明了一个拟度量空间是局部Yoneda完备的,当且仅当每个局部网都有一个d-极限。最后,我们证明了每一个拟度量空间都有一个局部Yoneda完备。
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Local Yoneda completions of quasi-metric spaces
Abstract In this paper, we study quasi-metric spaces using domain theory. Given a quasi-metric space (X,d), we use $({\bf B}(X,d),\leq^{d^{+}}\!)$ to denote the poset of formal balls of the associated quasi-metric space (X,d). We introduce the notion of local Yoneda-complete quasi-metric spaces in terms of domain-theoretic properties of $({\bf B}(X,d),\leq^{d^{+}}\!)$ . The manner in which this definition is obtained is inspired by Romaguera–Valero theorem and Kostanek–Waszkiewicz theorem. Furthermore, we obtain characterizations of local Yoneda-complete quasi-metric spaces via local nets in quasi-metric spaces. More precisely, we prove that a quasi-metric space is local Yoneda-complete if and only if every local net has a d-limit. Finally, we prove that every quasi-metric space has a local Yoneda completion.
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来源期刊
Mathematical Structures in Computer Science
Mathematical Structures in Computer Science 工程技术-计算机:理论方法
CiteScore
1.50
自引率
0.00%
发文量
30
审稿时长
12 months
期刊介绍: Mathematical Structures in Computer Science is a journal of theoretical computer science which focuses on the application of ideas from the structural side of mathematics and mathematical logic to computer science. The journal aims to bridge the gap between theoretical contributions and software design, publishing original papers of a high standard and broad surveys with original perspectives in all areas of computing, provided that ideas or results from logic, algebra, geometry, category theory or other areas of logic and mathematics form a basis for the work. The journal welcomes applications to computing based on the use of specific mathematical structures (e.g. topological and order-theoretic structures) as well as on proof-theoretic notions or results.
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