Borsuk–Ulam Theorem
- Natural & Formal Sciences -
Mathematics & Logic Dictionary
Definition
The statement that any continuous map f from the n-sphere S^n to Euclidean n-space R^n maps some pair of antipodal points x and −x to the same image point: f(x)=f(−x).
Borsuk–Ulam Theorem
- Mathematics & Logic -
Pure Mathematics Dictionary
Definition
A theorem in algebraic topology: any continuous map from the n-sphere S^n to Euclidean n-space R^n identifies at least one pair of antipodal points, i.e., there exists x in S^n with f(x)=f(−x).