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- Knaster–Tarski_theorem 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.".
- Knaster–Tarski_theorem wikiPageID "181417".
- Knaster–Tarski_theorem wikiPageRevisionID "605045549".
- Knaster–Tarski_theorem subject Category:Articles_containing_proofs.
- Knaster–Tarski_theorem subject Category:Fixed-point_theorems.
- Knaster–Tarski_theorem subject Category:Fixed_points_(mathematics).
- Knaster–Tarski_theorem subject Category:Order_theory.
- Knaster–Tarski_theorem subject Category:Theorems_in_the_foundations_of_mathematics.
- Knaster–Tarski_theorem 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.".
- Knaster–Tarski_theorem label "Fixpunktsatz von Tarski und Knaster".
- Knaster–Tarski_theorem label "Knaster–Tarski theorem".
- Knaster–Tarski_theorem label "Teorema de Knaster-Tarski".
- Knaster–Tarski_theorem label "Teorema di Knaster-Tarski".
- Knaster–Tarski_theorem label "Théorème de Knaster-Tarski".
- Knaster–Tarski_theorem label "Twierdzenie Knastera-Tarskiego o punkcie stałym".
- Knaster–Tarski_theorem label "Теорема Кнастера — Тарского".
- Knaster–Tarski_theorem label "克纳斯特－塔斯基定理".
- Knaster–Tarski_theorem sameAs Knaster%E2%80%93Tarski_theorem.
- Knaster–Tarski_theorem sameAs Fixpunktsatz_von_Tarski_und_Knaster.
- Knaster–Tarski_theorem sameAs Teorema_de_Knaster-Tarski.
- Knaster–Tarski_theorem sameAs Théorème_de_Knaster-Tarski.
- Knaster–Tarski_theorem sameAs Teorema_di_Knaster-Tarski.
- Knaster–Tarski_theorem sameAs Twierdzenie_Knastera-Tarskiego_o_punkcie_stałym.
- Knaster–Tarski_theorem sameAs Q609612.
- Knaster–Tarski_theorem sameAs Q609612.
- Knaster–Tarski_theorem wasDerivedFrom Knaster–Tarski_theorem?oldid=605045549.