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arXiv · 2407.09677

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

Andrea Ammerlaan·Ana Anušić·Logan C. Hoehn
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Abstract

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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Andrea Ammerlaan, Ana Anušić, Logan C. Hoehn. 2024-07-12. The Nadler-Quinn problem on accessible points of arc-like continua. https://arxiv.org/abs/2407.09677

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