On the closure of the diagonal of a $T_1$-space

On the closure of the diagonal of a $T_1$-space

Let X be a topological space. The closure of \Delta = {(x, x) : x \in X} in X \times X is a symmetric relation on X. We characterise those equivalence relations on an infinite set that arise as the closure of the diagonal with respect to a T_1-topology.

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Bibliographische Detailangaben
Hauptverfasser: Colasante, Maria-Luisa, van der Zypen, Dominic
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - General Topology
Mathematics - Logic
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Zusammenfassung:Let X be a topological space. The closure of \Delta = {(x, x) : x \in X} in X \times X is a symmetric relation on X. We characterise those equivalence relations on an infinite set that arise as the closure of the diagonal with respect to a T_1-topology.
DOI:10.48550/arxiv.0705.3877