弧状连续体可达点上的纳德勒-奎因问题

arXiv - MATH - General Topology Pub Date : 2024-07-12 DOI:arxiv-2407.09677

Andrea Ammerlaan, Ana Anušić, Logan C. Hoehn

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引用次数: 0

摘要

我们证明，如果 $X$ 是弧状连续统，那么对于 X$ 中的每个点 $x \来说，都有一个 $X$ 的平面嵌入，其中 $x$ 是一个可访问点。这回答了纳德勒在 1972 年提出的一个问题，即连续统理论中的纳德勒-奎因问题。为此，我们发展了区间映射的截断和等值因子理论。作为必然结果，我们回答了迈尔在 1982 年提出的关于不可分解弧状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 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 Mayer from 1982 about inequivalent plane embeddings of indecomposable arc-like continua.

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arXiv - MATH - General Topology

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