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Idealization of some weak separation axioms

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

An ideal is a nonempty collection of subsets closed under heredity and finite additivity. The aim of this paper is to unify some weak separation properties via topological ideals. We concentrate our attention on the separation axioms between $T_0$ and $T_2$. We prove that if $(X,τ,{\cal I})$ is a semi-Alexandroff $T_{\cal I}$-space and $\cal I$ is a $τ$-boundary, then $\cal I$ is completely codense.

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Francisco G. Arenas, Julian Dontchev, Maria Luz Puertas. 1998-10-12. Idealization of some weak separation axioms. https://arxiv.org/abs/math/9810075

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