Linked from

The 28 pages that link to Brouwer fixed-point theorem, each with the reason it gives.

• Banach fixed-point theoremCompared with: It guarantees existence by topology, without requiring a distance-shrinking map or uniqueness.

• Constructive proofCompared with: Its classical existence proof illustrates how a theorem can hold without yielding a general explicit fixed-point algorithm.

• Inverse function theoremCompared with: It gives global existence information, unlike the inverse function theorem's local uniqueness and structure.

• Kakutani fixed-point theoremCompared with: Brouwer handles single-valued continuous maps; Kakutani extends the guarantee to correspondences.

• Rouché's theoremCompared with: It is a topological existence theorem, not a complex-analytic zero-counting criterion.

• Lefschetz fixed-point theoremCompared with: It guarantees fixed points for a specific domain without computing a Lefschetz number.

• Boolean prime ideal theoremCompared with: Its proof and strength concern topological fixed points, not prime ideals or ultrafilters.

• Borsuk–Ulam theoremCompared with: It concerns a fixed point in a ball, whereas Borsuk–Ulam concerns equal values at opposite sphere points.

• Knaster–Tarski theoremCompared with: It relies on topology and continuity instead of lattice order and monotonicity.

• Poincaré–Birkhoff theoremCompared with: Brouwer’s result uses a ball and self-mapping condition rather than annular twist and rotation.

• Ryll-Nardzewski fixed-point theoremCompared with: Brouwer is finite-dimensional and concerns one map, unlike this common fixed-point result.

• Sharkovsky's theoremCompared with: It guarantees a fixed point from domain topology, whereas Sharkovsky’s theorem forces periods from an existing orbit.