Knaster–Tarski theorem
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 (w.r.t. ≤). Then the set of fixed points of f in L also forms a complete lattice under ≤. The theorem has important applications in formal semantics of programming languages and abstract interpretation.
Abstract interpretationAnne C. MorelBisimulationBronisław KnasterComplete latticeFixed-point theoremFixed point (mathematics)Interval propagationIntroduction to Lattices and OrderKleene fixed-point theoremKnaster-Tarski theoremLeast fixed pointList of functional programming topicsList of order theory topicsList of theoremsList of things named after Alfred TarskiMarket designModal μ-calculusParity gameSchröder–Bernstein theoremTarski's fixed point theoremTarski's theoremTarski-Knaster theoremTarski fixed point theoremTarski–Knaster theorem
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Knaster–Tarski theorem
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 (w.r.t. ≤). Then the set of fixed points of f in L also forms a complete lattice under ≤. The theorem has important applications in formal semantics of programming languages and abstract interpretation.
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Der Fixpunktsatz von Tarski un ...... em Gebiet der Verbandstheorie.
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El teorema de Knaster-Tarski, ...... rea de la teoría de retículos.
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Il teorema di Knaster-Tarski è un teorema di punto fisso.
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In the mathematical areas of o ...... then L is a complete lattice.
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Le théorème de Knaster-Tarski ...... slaw Knaster et Alfred Tarski.
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O Teorema de Knaster–Tarski, p ...... ão L é um reticulado completo.
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Twierdzenie Knastera-Tarskiego ...... szereg ważnych zastosowań w .
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Нехай D - , - неперервне відоб ...... якої справедлива формула: , де
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Теорема Кнастера — Тарского (т ...... нтике языков программирования.
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在数学领域序理论和格理论中，Knaster–Tarski 定 ...... 序保持函数 f : L → L 有不动点，则 L 是完全格。
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Der Fixpunktsatz von Tarski un ...... em Gebiet der Verbandstheorie.
@de
El teorema de Knaster-Tarski, ...... rea de la teoría de retículos.
@es
Il teorema di Knaster-Tarski è un teorema di punto fisso.
@it
In the mathematical areas of o ...... s and abstract interpretation.
@en
Le théorème de Knaster-Tarski ...... slaw Knaster et Alfred Tarski.
@fr
O Teorema de Knaster–Tarski, p ...... mbém é um reticulado completo.
@pt
Twierdzenie Knastera-Tarskiego ...... szereg ważnych zastosowań w .
@pl
Нехай D - , - неперервне відоб ...... якої справедлива формула: , де
@uk
Теорема Кнастера — Тарского (т ...... нтике языков программирования.
@ru
在数学领域序理论和格理论中，Knaster–Tarski 定 ...... 序保持函数 f : L → L 有不动点，则 L 是完全格。
@zh
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Fixpunktsatz von Tarski und Knaster
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Knaster–Tarski theorem
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Teorema de Knaster-Tarski
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Teorema de Knaster–Tarski
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Teorema di Knaster-Tarski
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Théorème de Knaster-Tarski
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Twierdzenie Knastera-Tarskiego o punkcie stałym
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Теорема Кнастера — Тарского
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Теорема Кнастера — Тарського
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克纳斯特－塔斯基定理
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