Semi-Kelley compactifications of $(0,1]$

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.