Τ-quasi-Cauchy spaces - a non-symmetric theory of completeness and completion

IF 0.6 Q3 MATHEMATICS

Applied general topology Pub Date : 2023-04-05 DOI:10.4995/agt.2023.18783

G. Jäger

引用次数: 0

Abstract

Based on the concept of Cauchy pair Τ-filters, we develop an axiomatic theory of completeness for non-symmetric spaces, such as Τ-quasi-uniform (limit) spaces or L-metric spaces. We show that the category of Τ-quasi-Cauchy spaces is topological and Cartesian closed and we construct a finest completion for a non-complete Τ-quasi-Cauchy space. In the special case of symmetry, Τ-quasi-Cauchy spaces can be identified with Τ-Cauchy spaces.

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Τ-quasi-Cauchy空间-完备和补全的非对称理论

基于柯西对Τ-filters的概念，我们发展了非对称空间完备性的公理理论，如Τ-quasi-uniform(极限)空间或l -度量空间。我们证明了Τ-quasi-Cauchy空间的范畴是拓扑和笛卡尔闭的，并构造了一个非完备Τ-quasi-Cauchy空间的最优完备。在对称的特殊情况下，Τ-quasi-Cauchy空间可以与Τ-Cauchy空间识别。

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

Applied general topology MATHEMATICS-

CiteScore

1.20

自引率

25.00%

发文量

审稿时长

15 weeks

期刊介绍： The international journal Applied General Topology publishes only original research papers related to the interactions between General Topology and other mathematical disciplines as well as topological results with applications to other areas of Science, and the development of topological theories of sufficiently general relevance to allow for future applications. Submissions are strictly refereed. Contributions, which should be in English, can be sent either to the appropriate member of the Editorial Board or to one of the Editors-in-Chief. All papers are reviewed in Mathematical Reviews and Zentralblatt für Mathematik.