Lusternik–Schnirelmann theorem

In mathematics, the Lusternik–Schnirelmann theorem, aka Lusternik–Schnirelmann–Borsuk theorem or LSB theorem, says as follows.

If the sphere Sn is covered by n + 1 closed sets, then one of these sets contains a pair (x, −x) of antipodal points.

It is named after Lazar Lyusternik and Lev Schnirelmann, who published it in 1930.

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