  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.
