The fixed point property for small sets (Q1262328)
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scientific article; zbMATH DE number 4123783
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The fixed point property for small sets |
scientific article; zbMATH DE number 4123783 |
Statements
The fixed point property for small sets (English)
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1989
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An ordered set P has the fixed point property if every order-preserving self-mapping of P has a fixed point. An element \(x\equiv P\) is irreducible in P if it has unique upper cover or unique lower cover. Main theorem: There exist exactly eleven (up to isomorphism and duality) ordered sets of size \(\leq 10\) with a fixed point property and containing no irreducible elements. These are the singleton and ten sets which the author exactly describes by figures.
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dismantability
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fixed point property
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irreducible elements
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