Pseudocomplements of closure operators on posets (Q1598820)
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scientific article; zbMATH DE number 1746256
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Pseudocomplements of closure operators on posets |
scientific article; zbMATH DE number 1746256 |
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Pseudocomplements of closure operators on posets (English)
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28 May 2002
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The author gives some new results of pseudocomplementation in the more general setting of closure operators on mere posets. He proves that if \(P\) is a meet-continuous meet-semilattice, then \(\text{uco}(P)\) is a pseudocoplemented complete lattice. Further he proves the complementary result: Closure operators on a directed-complete poset which is transfinitely generated by maximal lower bounds from its set of completely meet-irreducible elements, form a pseudocoplemented complete lattice.
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pseudocomplement
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closure operator
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poset
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meet-continuity
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maximal lower bound
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0.8139076232910156
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0.7783771753311157
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