Planarity of compactifications of $\mathbb{R}$ with arc-like remainder
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912052183826432 |
|---|---|
| author | Ammerlaan, Andrea Hoehn, Logan C. |
| author_facet | Ammerlaan, Andrea Hoehn, Logan C. |
| contents | We show that if $X$ is an arc-like continuum, then any continuum which is the union of $X$ and a ray $R$ such that $X \cap R = \emptyset$ and $\overline{R} \setminus R \subseteq X$ can be embedded in the plane $\mathbb{R}^2$. Further, we prove that any compactification of a line with remainder $X$ is also embeddable in $\mathbb{R}^2$ -- answering a question of Sam B. Nadler from 1972. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_20455 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Planarity of compactifications of $\mathbb{R}$ with arc-like remainder Ammerlaan, Andrea Hoehn, Logan C. General Topology Primary 54F15, 54C25, Secondary 54F50, 54D35 We show that if $X$ is an arc-like continuum, then any continuum which is the union of $X$ and a ray $R$ such that $X \cap R = \emptyset$ and $\overline{R} \setminus R \subseteq X$ can be embedded in the plane $\mathbb{R}^2$. Further, we prove that any compactification of a line with remainder $X$ is also embeddable in $\mathbb{R}^2$ -- answering a question of Sam B. Nadler from 1972. |
| title | Planarity of compactifications of $\mathbb{R}$ with arc-like remainder |
| topic | General Topology Primary 54F15, 54C25, Secondary 54F50, 54D35 |
| url | https://arxiv.org/abs/2409.20455 |