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IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-10-16 DOI:10.1016/j.topol.2024.109105

Taras Banakh

引用次数: 0

摘要

按照威尔-布赖恩（Will Brian）的定义，如果 X 中所有半径为正 r 的非空球的心数都是 2，直径都是 2r，那么这个度量空间 X 就是 Banakh 空间。Banakh空间的标准例子是实线的子群。在本文中，我们研究了巴纳赫空间的几何，描述了与实线子群等距的巴纳赫空间的特征，还构造了不嵌入实线且具有规定距离集 d[X2] 的巴纳赫空间 X。

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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Banakh spaces and their geometry

Following Will Brian, we define a metric space X to be Banakh if all nonempty spheres of positive radius r in X have cardinality 2 and diameter 2r. Standard examples of Banakh spaces are subgroups of the real line. In this paper we study the geometry of Banakh spaces, characterize Banakh spaces which are isometric to subgroups of the real line, and also construct Banakh spaces X which do not embed into the real line and have a prescribed distance set

d [X^{2}]

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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.