2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77542The 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 $(X,τ)$ a $T_{κ,ξ}$-space if every compact subset of $X$ with cardinality $\leq κ$ is $ξ$-closed, where $ξ$ is a general closure operator. We concentrate our attention mostly on two new concepts: kd-spaces and $T_{1/3}$-spaces.11 pagesGeneral Topology54A05; 54D10; 54D30; 54H05text