The ε-approximated complete invariance property

IF 0.6 Q3 MATHEMATICS

Applied general topology Pub Date : 2022-10-03 DOI:10.4995/agt.2022.16641

G. García

引用次数: 0

Abstract

In the present paper we introduce a generalization of the complete invariance property (CIP) for metric spaces, which we will call the ε-approximated complete invariance property (ε-ACIP). For our goals, we will use the so called degree of nondensifiability (DND) which, roughly speaking, measures (in the specified sense) the distance from a bounded metric space to its class of Peano continua. Our main result relates the ε-ACIP with the DND and, in particular, proves that a densifiable metric space has the ε-ACIP for each ε>0. Also, some essentials differences between the CIP and the ε-ACIP are shown.

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ε-近似完全不变性

本文对度量空间的完全不变性(CIP)进行了推广，我们将其称为ε-近似完全不变性(ε-ACIP)。为了我们的目标，我们将使用所谓的非致密度(DND)，粗略地说，它(在特定意义上)度量从有界度量空间到它的Peano连续体类的距离。我们的主要结果将ε- acip与DND联系起来，特别是证明了一个可密度量空间对于ε>0都具有ε- acip。此外，还指出了CIP与ε-ACIP之间的一些本质区别。

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.