areas of order and lattice theory, the Knaster–Tarski theorem, named after Bronisław Knaster and Alfred Tarski, states the following: Let (L, ≤) be a...

closed fields Knaster–Tarski theorem (sometimes referred to as Tarski's fixed point theorem) Tarski–Seidenberg theorem Some fixed point theorems, usually variants...

Fixed-point theorems in infinite-dimensional spaces Injective metric space Kakutani fixed-point theorem Kleene fixed-point theorem Knaster–Tarski theorem Lefschetz...

Łoś–Tarski preservation theorem Knaster–Tarski theorem (sometimes referred to as Tarski's fixed point theorem) Tarski's undefinability theorem Tarski–Seidenberg...

lists, in domain theory. Kleene fixed-point theorem for Scott-continuous functions Knaster–Tarski theorem for complete lattices Nicolas Bourbaki (1949)...

axiom of choice). The principle is also called the Hausdorff maximality theorem or the Kuratowski lemma (Kelley 1955:33). The Hausdorff maximal principle...

In mathematics, the Boolean prime ideal theorem states that ideals in a Boolean algebra can be extended to prime ideals. A variation of this statement...

antichain in a partially ordered set is known as its width. By Dilworth's theorem, this also equals the minimum number of chains (totally ordered subsets)...

take a particularly simple form in this case. An example is the Knaster–Tarski theorem, which states that the set of fixed points of a monotone function...

complete partial order, (d)cpo Bounded complete Complete lattice Knaster–Tarski theorem Infinite divisibility Heyting algebra Relatively complemented lattice...

In mathematics, Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under...

mathematics, in the areas of order theory and combinatorics, Dilworth's theorem states that, in any finite partially ordered set, the maximum size of an...

ideal theorem Cantor–Bernstein theorem Cantor's isomorphism theorem Dilworth's theorem Dushnik–Miller theorem Hausdorff maximal principle Knaster–Tarski theorem...

Hausdorff maximality theorem (set theory) Kleene fixed-point theorem (order theory) Knaster–Tarski theorem (order theory) Kruskal's tree theorem (order theory)...

In set theory and order theory, the Cantor–Bernstein theorem states that the cardinality of the second type class, the class of countable order types...

problemsPages displaying wikidata descriptions as a fallback Knaster–Tarski theorem – Theorem in order and lattice theory Sutherland, Wilson A. (1975). Introduction...

Bronisław Knaster (22 May 1893 – 3 November 1980) was a Polish mathematician; from 1939 a university professor in Lwów and from 1945 in Wrocław. In 1945...

mathematics, in the areas of order theory and combinatorics, Mirsky's theorem characterizes the height of any finite partially ordered set in terms of...

countable intersections of open sets are open Speer 2007, Theorem 7. Arenas 1999, Theorem 2.2. Erné, M. "The ABC of order and topology" (PDF)., page...

ideal theorem Cantor–Bernstein theorem Cantor's isomorphism theorem Dilworth's theorem Dushnik–Miller theorem Hausdorff maximal principle Knaster–Tarski theorem...

ideal theorem Cantor–Bernstein theorem Cantor's isomorphism theorem Dilworth's theorem Dushnik–Miller theorem Hausdorff maximal principle Knaster–Tarski theorem...

North-Holland (1984) This is a strengthening of the Knaster–Tarski theorem sometimes referred to as "Pataraia’s theorem". For example, see Section 4.1 of "Realizability...

algebra De Morgan algebra First-order logic Heyting algebra Lindenbaum–Tarski algebra Skew Boolean algebra Algebraic normal form Boolean conjunctive query...

{\displaystyle (Tu-Tv,u-v)\geq 0\quad \forall u,v\in X.} Kachurovskii's theorem shows that convex functions on Banach spaces have monotonic operators as...

ideal theorem Cantor–Bernstein theorem Cantor's isomorphism theorem Dilworth's theorem Dushnik–Miller theorem Hausdorff maximal principle Knaster–Tarski theorem...

& Tamassia (1995a), Theorem 9, p. 118; Baker, Fishburn & Roberts (1971), theorem 4.1, page 18. Garg & Tamassia (1995a), Theorem 15, p. 125; Bertolazzi...

an inherent asymmetry between the two operators, while the axioms and theorems of Boolean algebra express the symmetry of the theory described by the...

partial orders, called distributive lattices; see Birkhoff's representation theorem. Sequence A001035 in OEIS gives the number of partial orders on a set of...

must preserve the existence of least elements. By Cantor's isomorphism theorem, every unbounded countable dense linear order is isomorphic to the ordering...

ideal theorem Cantor–Bernstein theorem Cantor's isomorphism theorem Dilworth's theorem Dushnik–Miller theorem Hausdorff maximal principle Knaster–Tarski theorem...