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Unification approach to the separation axioms between $T_0$ and completely Hausdorff

Francisco G. Arenas·Julian Dontchev·Maria Luz Puertas
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Abstract

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 $(X,τ)$ 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.

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Francisco G. Arenas, Julian Dontchev, Maria Luz Puertas. 1998-10-12. Unification approach to the separation axioms between $T_0$ and completely Hausdorff. https://arxiv.org/abs/math/9810074

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