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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.09677 |
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| _version_ | 1866916322330279936 |
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| author | Ammerlaan, Andrea Anušić, Ana Hoehn, Logan C. |
| author_facet | Ammerlaan, Andrea Anušić, Ana Hoehn, Logan C. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09677 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Nadler-Quinn problem on accessible points of arc-like continua Ammerlaan, Andrea Anušić, Ana Hoehn, Logan C. General Topology 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. |
| title | The Nadler-Quinn problem on accessible points of arc-like continua |
| topic | General Topology |
| url | https://arxiv.org/abs/2407.09677 |