arXiv subjects
Publications and source records attributed to Francisco G. Arenas.
Recently, Mršević and Reilly discussed some covering properties of a topological space and its associated $α$-topology in both topological and bitopological ways. The main aim of this paper is to investigate some common and controversial covering properties of $\cal T$ and ${\cal T}^α$.
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.
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.