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The 24 pages that link to Fixed-point theorem, each with the reason it gives.

• ContinuityRelated: 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.

• John NashNarrower topic: Nash used a fixed-point argument to prove equilibrium existence.

• Connected spaceRelated: Connectedness is among the hypotheses that make several classical fixed-point results possible.

• Supremum normNarrower topic: Contraction-based fixed-point proofs use normed function spaces and often the supremum norm.

• 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.

• L. E. J. BrouwerNarrower topic: Brouwer’s theorem became a defining example in a broad family of mathematical results.

• Monotone functionRelated: Monotone maps on ordered spaces often yield fixed points under suitable completeness conditions.

• Transfinite recursionCompared with: Fixed-point methods characterize self-consistent values, whereas recursion specifies values from earlier stages.

• David GaleRelated: Fixed-point methods underpin existence proofs for equilibria in mathematical economics.

• Peano existence theoremNarrower topic: Alternative existence proofs recast the differential equation as a fixed-point problem.

• Existence theoremBroader topic: It guarantees a solution by proving that a suitable function has a fixed point.

• 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.

• Kleene's recursion theoremNarrower topic: The theorem is a computability-specific fixed-point result, with equality understood through program behavior.

• 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.