[0,1]上带区间值函数的逆极限可链性条件

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-04-30 DOI:10.1016/j.topol.2024.108933

M.M. Marsh

引用次数: 0

摘要

对于[0,1]上带区间值函数的逆序，我们建立了逆极限空间可链性的结合函数的必要条件。我们还根据结合函数 fi 和诱导函数 Fn:[0,1]→G′(f1,...fn-1) 的性质，描述了逆极限在这种情况下的可链性。在这两种情况下，这些性质都与当每个图 G(fi) 都是可链时，如何在与逆序相关的局部图中出现三足鼎立有关。

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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Conditions for chainability of inverse limits on [0,1] with interval-valued functions

For an inverse sequence on $[0, 1]$ with interval-valued functions, we establish necessary conditions on the bonding functions for chainability of the inverse limit space. We also characterize chainability of the inverse limit in this setting in terms of properties of the bonding functions $f_{i}$ and the induced functions $F_{n} : [0, 1] \to G^{'} (f_{1}, \dots, f_{n - 1})$ . The properties, in both cases, are related to how triods arise in the partial graphs associated with the inverse sequence when each graph $G (f_{i})$ is chainable.

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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.