On the probabilistic metrizability of approach spaces

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-10-28 DOI:10.1016/j.topol.2024.109113

Hongliang Lai , Lili Shen , Junche Yu

引用次数: 0

Abstract

We investigate approach spaces generated by probabilistic metric spaces with respect to a continuous t-norm ⁎ on the unit interval

[0, 1]

. Let

k^{⁎}

be the supremum of the idempotent elements of ⁎ in

[0, 1)

. It is shown that if

k^{⁎} = 1

(resp.

k^{⁎} < 1

), then an approach space is probabilistic metrizable with respect to ⁎ if and only if it is probabilistic metrizable with respect to the minimum (resp. product) t-norm.

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论方法空间的概率元可操作性

我们研究由概率度量空间产生的、关于单位区间 [0,1] 上连续 t 准则⁎ 的方法空间。设 k⁎ 是⁎ 在 [0,1] 中的幂元素的上集。研究表明，如果 k⁎=1 (resp. k⁎<1)，那么当且仅当一个方法空间在最小（resp. product）t-norm 方面是可概率元空间时，它在⁎ 方面才是可概率元空间。

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.