KnowraFixed-point theoremLinked fromLinked fromThe 24 pages that link to Fixed-point theorem, each with the reason it gives.All 24Broader topic 1Related 17Narrower topic 5Compared with 1ContinuityRelated: Continuity is a key hypothesis in classical fixed-point results such as Brouwer’s theorem.Intermediate value theoremRelated: Intermediate-value arguments prove fixed points for continuous maps of intervals.Connected spaceRelated: Connectedness is among the hypotheses that make several classical fixed-point results possible.Mathematical economicsRelated: Existence proofs for economic equilibria often rely on fixed-point results.Integral equationRelated: Rewriting the equation as a fixed-point problem enables existence proofs.Diagonal argumentRelated: Self-reference in Gödel's proof is often formalized through a fixed-point construction.Monotone functionRelated: Monotone maps on ordered spaces often yield fixed points under suitable completeness conditions.David GaleRelated: Fixed-point methods underpin existence proofs for equilibria in mathematical economics.Gérard DebreuRelated: Fixed-point methods provide a mathematical route to equilibrium existence.Lwów School of MathematicsRelated: Fixed-point methods became a distinctive part of the school’s functional analysis.Order theoryRelated: Order-theoretic hypotheses can ensure monotone maps have fixed points.Borsuk–Ulam theoremRelated: Brouwer’s fixed-point theorem yields a route to the antipodal coincidence result.General topologyRelated: Topological hypotheses can guarantee fixed points without requiring explicit solutions.Löb's theoremRelated: The diagonal lemma is a logical fixed-point result that supports Löb’s self-reference.John Forbes Nash Jr.Related: Fixed-point reasoning underlies the existence proof for Nash equilibrium.Join and meetRelated: Complete lattices supply the order structure used by the Knaster–Tarski fixed-point theorem.Sharkovsky's theoremRelated: Period one is the simplest periodic behavior and appears last in Sharkovsky’s ordering.
KnowraFixed-point theoremLinked fromLinked fromThe 24 pages that link to Fixed-point theorem, each with the reason it gives.All 24Broader topic 1Related 17Narrower topic 5Compared with 1ContinuityRelated: Continuity is a key hypothesis in classical fixed-point results such as Brouwer’s theorem.Intermediate value theoremRelated: Intermediate-value arguments prove fixed points for continuous maps of intervals.Connected spaceRelated: Connectedness is among the hypotheses that make several classical fixed-point results possible.Mathematical economicsRelated: Existence proofs for economic equilibria often rely on fixed-point results.Integral equationRelated: Rewriting the equation as a fixed-point problem enables existence proofs.Diagonal argumentRelated: Self-reference in Gödel's proof is often formalized through a fixed-point construction.Monotone functionRelated: Monotone maps on ordered spaces often yield fixed points under suitable completeness conditions.David GaleRelated: Fixed-point methods underpin existence proofs for equilibria in mathematical economics.Gérard DebreuRelated: Fixed-point methods provide a mathematical route to equilibrium existence.Lwów School of MathematicsRelated: Fixed-point methods became a distinctive part of the school’s functional analysis.Order theoryRelated: Order-theoretic hypotheses can ensure monotone maps have fixed points.Borsuk–Ulam theoremRelated: Brouwer’s fixed-point theorem yields a route to the antipodal coincidence result.General topologyRelated: Topological hypotheses can guarantee fixed points without requiring explicit solutions.Löb's theoremRelated: The diagonal lemma is a logical fixed-point result that supports Löb’s self-reference.John Forbes Nash Jr.Related: Fixed-point reasoning underlies the existence proof for Nash equilibrium.Join and meetRelated: Complete lattices supply the order structure used by the Knaster–Tarski fixed-point theorem.Sharkovsky's theoremRelated: Period one is the simplest periodic behavior and appears last in Sharkovsky’s ordering.