Metric duality for Abelian groups

IF 0.5 4区数学 Q3 MATHEMATICS Topology and its Applications Pub Date : 2025-02-01 DOI:10.1016/j.topol.2024.109155

Piotr Niemiec

引用次数: 0

Abstract

The main aim of the paper is to introduce the concept of metric duality in the category of topological Abelian groups that extends the classical notion of duality for normed vector spaces and behaves quite nicely for LCA groups (equipped with nice metrics). In particular, it is shown that each Polish LCA group admits a reflexive proper metric and, more generally, all LCA groups possess reflexive (proper) metric structures.

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阿贝尔群的度量对偶性

本文的主要目的是在拓扑阿贝尔群范畴中引入度量对偶的概念，它扩展了经典对偶概念在赋范向量空间中的应用，并且在LCA群（具有良好度量）中表现得很好。特别地，我们证明了每个波兰LCA群都有一个自反的固有度规，更一般地说，所有LCA群都具有自反（固有）度规结构。

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.

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