类弧连续体可达点上的Nadler-Quinn问题

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-08-20 DOI:10.1016/j.aim.2025.110491

Andrea Ammerlaan , Ana Anušić , Logan C. Hoehn

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引用次数: 0

摘要

我们证明了如果X是一个类弧连续体，那么对于每个点X∈X，存在X的一个平面嵌入，其中X是一个可达点。这回答了Sam B. Nadler在1972年提出的一个问题，这个问题后来被称为连续统理论中的Nadler- quinn问题。为此，我们发展了区间映射的截断和等高线分解理论。作为推论，我们回答了1982年J.C. Mayer关于不可分解的类弧连续体的不等价平面嵌入的问题。

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The Nadler-Quinn problem on accessible points of arc-like continua

We show that if X is an arc-like continuum, then for every point

x \in X

there is a plane embedding of X in which x is an accessible point. This answers a question posed by Sam B. Nadler in 1972, which has become known as the Nadler-Quinn problem in continuum theory. Towards this end, we develop the theories of truncations and contour factorizations of interval maps. As a corollary, we answer a question of J.C. Mayer from 1982 about inequivalent plane embeddings of indecomposable arc-like continua.

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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.