Every continuous map must identify a pair of antipodal points.
Borsuk-Ulam Theorem
See also
Antipodal PointsExplore with Wolfram|Alpha
References
Dodson, C. T. J. and Parker, P. E. A User's Guide to Algebraic Topology. Dordrecht, Netherlands: Kluwer, pp. 121 and 284, 1997.Referenced on Wolfram|Alpha
Borsuk-Ulam TheoremCite this as:
Weisstein, Eric W. "Borsuk-Ulam Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Borsuk-UlamTheorem.html