Every countable lattice is a retract of a direct product of chains (Q797605)
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scientific article; zbMATH DE number 3867394
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Every countable lattice is a retract of a direct product of chains |
scientific article; zbMATH DE number 3867394 |
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Every countable lattice is a retract of a direct product of chains (English)
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1984
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The authors prove that every countably lattice is retract (i.e., idempotent endomorphic image) of a direct product of the following ordered sets: the two- and three-element sets, the positive and negative integers and their direct sum. This result can be regarded as a negative one, for it shows how complicated a retract can be. The proof goes via Boolean algebras. Two basic concepts are used: gaps and selection property which might be useful in other research.
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countably lattice
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retract
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idempotent endomorphic image
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gaps
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selection property
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