Semi-Kelley compactifications of $(0,1]$
Volume 168 / 2022
Colloquium Mathematicum 168 (2022), 325-340
MSC: Primary 54F15, 54F65; Secondary 54F50, 54D35, 54D40.
DOI: 10.4064/cm8192-4-2021
Published online: 7 February 2022
Abstract
We characterize the semi-Kelley compactifications of $(0,1]$ with remainder being an arc or a simple closed curve. We also prove that there are no semi-Kelley compactifications of $(0,1]$ with remainder being a triod. Finally, we prove that if $X$ is a semi-Kelley compactification of $(0,1]$ with remainder being a Peano continuum $G$, then $G$ is an arc or a simple closed curve.
