Non-Hausdorff $T_1$ properties
Volume 181 / 2026
Colloquium Mathematicum 181 (2026), 1-16
MSC: Primary 54D10
DOI: 10.4064/cm9556-4-2026
Published online: 11 June 2026
Abstract
Several weakenings of the $T_2$ property for topological spaces, including $k$-Hausdorff, $KC$, weakly Hausdorff, semi-Hausdorff, $RC$, and $US$, have been studied by mathematicians. Here we provide a complete survey of how these properties do or do not relate to one another, including several new results to fill in the gaps in the existing literature, motivated by the use of a community-maintained database of topological spaces and their properties.
