Perfectly supportable semigroups are \(\sigma\)-discrete in each Hausdorff shift-invariant topology (Q2851043)
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scientific article; zbMATH DE number 6213276
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Perfectly supportable semigroups are \(\sigma\)-discrete in each Hausdorff shift-invariant topology |
scientific article; zbMATH DE number 6213276 |
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2 October 2013
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semi-Zariski topology
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supt-perfect semigroup
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\(\sigma \)-discrete space
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group of finitely supported permutations
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semigroup of finitely supported relations
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Perfectly supportable semigroups are \(\sigma\)-discrete in each Hausdorff shift-invariant topology (English)
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The authors introduce and study a wide class of semigroups, that they call (perfectly) supportable, which are \(\sigma\)-discrete in any Hausdorff topology \(\tau\) such that the semigroup operation is separately continuous in \(\tau\). Typical examples of supportable semigroups are the semigroup \(\mathrm{Rel}(X)\) of all relations on a set \(X\) with the operation of composition of relations and its subgroup \(\mathrm{Sym}(X)\) of all bijections on \(X\).
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