Accessibility of countable sets in plane embeddings of arc-like continua
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914883537207296 |
|---|---|
| author | Anušić, Ana Hoehn, Logan C. |
| author_facet | Anušić, Ana Hoehn, Logan C. |
| contents | We consider the problem of finding embeddings of arc-like continua in the plane for which each point in a given subset is accessible. We establish that, under certain conditions on an inverse system of arcs, there exists a plane embedding of the inverse limit for which each point of a given countable set is accessible. As an application, we show that for any Knaster continuum $K$, and any countable collection $\mathcal{C}$ of composants of $K$, there exists a plane embedding of $K$ in which every point in the union of the composants in $\mathcal{C}$ is accessible. We also exhibit new embeddings of the Knaster buckethandle continuum $K$ in the plane which are attractors of plane homeomorphisms, and for which the restriction of the plane homeomorphism to the attractor is conjugate to a power of the standard shift map on $K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16792 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Accessibility of countable sets in plane embeddings of arc-like continua Anušić, Ana Hoehn, Logan C. General Topology Dynamical Systems Primary 54F15, 54C25, Secondary 54F50, 37B45, 37E30 We consider the problem of finding embeddings of arc-like continua in the plane for which each point in a given subset is accessible. We establish that, under certain conditions on an inverse system of arcs, there exists a plane embedding of the inverse limit for which each point of a given countable set is accessible. As an application, we show that for any Knaster continuum $K$, and any countable collection $\mathcal{C}$ of composants of $K$, there exists a plane embedding of $K$ in which every point in the union of the composants in $\mathcal{C}$ is accessible. We also exhibit new embeddings of the Knaster buckethandle continuum $K$ in the plane which are attractors of plane homeomorphisms, and for which the restriction of the plane homeomorphism to the attractor is conjugate to a power of the standard shift map on $K$. |
| title | Accessibility of countable sets in plane embeddings of arc-like continua |
| topic | General Topology Dynamical Systems Primary 54F15, 54C25, Secondary 54F50, 37B45, 37E30 |
| url | https://arxiv.org/abs/2407.16792 |