KnowraBorsuk–Ulam theoremLinked fromLinked fromThe 4 pages that link to Borsuk–Ulam theorem, each with the reason it gives.All 4Related 4Brouwer fixed-point theoremRelated: It is a neighboring topological existence theorem with closely related sphere arguments.Algebraic topologyRelated: It illustrates how topological obstruction arguments yield geometric and combinatorial conclusions.Connected spaceRelated: Its topological proof uses connectedness-related ideas to establish an unavoidable coincidence.Ham sandwich theoremRelated: Its antipodal-point guarantee yields a hyperplane that bisects all n measures.