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Planarity of compactifications of $\mathbb{R}$ with arc-like remainder
- Publication Year :
- 2024
-
Abstract
- 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.<br />Comment: 7 pages, 2 figures
- Subjects :
- Mathematics - General Topology
Primary 54F15, 54C25, Secondary 54F50, 54D35
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2409.20455
- Document Type :
- Working Paper