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- Q609612 subject Q18550470.
- Q609612 subject Q7452041.
- Q609612 subject Q8266681.
- Q609612 subject Q8460852.
- Q609612 subject Q8460857.
- Q609612 abstract "In the mathematical areas of order and lattice theory, the Knaster–Tarski theorem, named after Bronisław Knaster and Alfred Tarski, states the following:Let L be a complete lattice and let f : L → L be an order-preserving function. Then the set of fixed points of f in L is also a complete lattice.It was Tarski who stated the result in its most general form, and so the theorem is often known as Tarski's fixed point theorem. Some time earlier, Knaster and Tarski established the result for the special case where L is the lattice of subsets of a set, the power set lattice.The theorem has important applications in formal semantics of programming languages and abstract interpretation.A kind of converse of this theorem was proved by Anne C. Davis: If every order preserving function f : L → L on a lattice L has a fixed point, then L is a complete lattice.".
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- Q609612 wikiPageWikiLink Q7452041.
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- Q609612 wikiPageWikiLink Q8460852.
- Q609612 wikiPageWikiLink Q8460857.
- Q609612 comment "In the mathematical areas of order and lattice theory, the Knaster–Tarski theorem, named after Bronisław Knaster and Alfred Tarski, states the following:Let L be a complete lattice and let f : L → L be an order-preserving function. Then the set of fixed points of f in L is also a complete lattice.It was Tarski who stated the result in its most general form, and so the theorem is often known as Tarski's fixed point theorem.".
- Q609612 label "Knaster–Tarski theorem".