If a sphere is covered by three closed sets, then one of them must contain a pair of antipodal points.
Lyusternik-Schnirelmann Theorem
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References
Dodson, C. T. J. and Parker, P. E. A User's Guide to Algebraic Topology. Dordrecht, Netherlands: Kluwer, pp. 122 and 284, 1997.Referenced on Wolfram|Alpha
Lyusternik-Schnirelmann TheoremCite this as:
Weisstein, Eric W. "Lyusternik-Schnirelmann Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Lyusternik-SchnirelmannTheorem.html