On the closure of the diagonal of a \(T_1\)-space (Q941438)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the closure of the diagonal of a \(T_1\)-space |
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On the closure of the diagonal of a \(T_1\)-space (English)
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1 September 2008
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Let \(X\) be a topological space. The closure of \(\Delta=\{(x, x): x\in X\}\) in \(X\times X\) is a symmetric relation on \(X\). The equivalence relations on an infinite set that arise as the closure of the diagonal with respect to a \(T_{1}\)-topology are characterized.
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diagonal
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equivalence relation
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separation
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\(T_{1}\)-space
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