度量空间上的抗吸收三元运算

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-02-01 DOI:10.1016/j.topol.2024.109153

Leonid V. Kovalev

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引用次数: 0

摘要

已知度量空间中值型三元运算的存在性对空间的几何有许多含义。对于这样的操作，如果三个参数中的两个一致，它们也与操作的输出一致。我们考虑具有相反性质的三元操作：如果两个参数重合，则输出等于第三个参数。这种操作的存在是空间绝对收缩的必要条件。

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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Anti-absorbing ternary operations on metric spaces

The existence of a median-type ternary operation on a metric space is known to have a number of implications for the geometry of the space. For such operations, if two of the three arguments coincide, they also coincide with the output of the operation. We consider ternary operations with the opposite property: if two of the arguments coincide, the output is equal to the third one. The existence of such an operation is a necessary condition for the space to be an absolute retract.

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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.