Non-Hausdorff $T_1$ Properties

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.