Endpoints of smooth plane dendroids
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914923270897664 |
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| author | Lipham, David S. |
| author_facet | Lipham, David S. |
| contents | Let $X$ be a smooth dendroid in the plane $\mathbb R^2$. We show that each endpoint of $X$ is arcwise accessible from $\mathbb R^2\setminus X$, and that the space of endpoints $E(X)$ has the property of a circle. In the event that $E(X)$ is connected, we call $X$ a *Bellamy dendroid*. We prove that if $E(X)$ is 1-dimensional, then $X$ contains a Bellamy dendroid or a Cantor set of arcs. In particular, if $E(X)$ totally disconnected and 1-dimensional, then $X$ is non-Suslinian. An example is constructed to show that this is false outside the plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01706 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Endpoints of smooth plane dendroids Lipham, David S. General Topology 54F15, 54F45, 54F50 Let $X$ be a smooth dendroid in the plane $\mathbb R^2$. We show that each endpoint of $X$ is arcwise accessible from $\mathbb R^2\setminus X$, and that the space of endpoints $E(X)$ has the property of a circle. In the event that $E(X)$ is connected, we call $X$ a *Bellamy dendroid*. We prove that if $E(X)$ is 1-dimensional, then $X$ contains a Bellamy dendroid or a Cantor set of arcs. In particular, if $E(X)$ totally disconnected and 1-dimensional, then $X$ is non-Suslinian. An example is constructed to show that this is false outside the plane. |
| title | Endpoints of smooth plane dendroids |
| topic | General Topology 54F15, 54F45, 54F50 |
| url | https://arxiv.org/abs/2405.01706 |