The aim of this paper is to introduce a new weak separation axiom that generalizes the separation properties between $T_1$ and completely Hausdorff. We call a topological space $(X,\tau)$ a $T_{ \kappa,\xi}$-space if every compact subset of $X$ with cardinality $\leq \kappa$ is $\xi$-closed, where $\xi$ is a general closure operator. We concentrate our attention mostly on two new concepts: kd-spaces and $T_{ 1/3}$-spaces.
Categories: math.GN