In mathematics, Sperner's lemma is a combinatorial result on colorings of triangulations, analogous to the Brouwer fixed point theorem, which is equivalent...

named after Emanuel Sperner, who published it in 1928. This result is sometimes called Sperner's lemma, but the name "Sperner's lemma" also refers to an...

Knaster, Kuratowski and Mazurkiewicz. The KKM lemma can be proved from Sperner's lemma and can be used to prove the Brouwer fixed-point theorem. Let Δ n −...

of certain combinatorial structures. For example, in the proofs of Sperner's lemma and the mountain climbing problem the geometric properties of the formula...

generalizations, including the Sperner property of a partially ordered set. Sperner's lemma, from 1928, states that every Sperner coloring of a triangulation...

Poincaré's lemma Riesz's lemma Schur's lemma Schwarz's lemma Sperner's lemma Urysohn's lemma Vitali covering lemma Yoneda's lemma Zorn's lemma While these...

{\displaystyle f(P)_{j}\leq P_{j}.} By construction, this is a Sperner coloring. Hence, by Sperner's lemma, there is an n-dimensional simplex whose vertices are...

JSTOR 2320587 Jarvis, Tyler; Tanton, James (2004), "The Hairy Ball Theorem via Sperner's Lemma", American Mathematical Monthly, 111 (7): 599–603, doi:10.1080/00029890...

Francis Edward (2013), "A Borsuk–Ulam equivalent that directly implies Sperner's lemma", The American Mathematical Monthly, 120 (4): 346–354, doi:10.4169/amer...

Francis Edward (2013), "A Borsuk–Ulam equivalent that directly implies Sperner's lemma", The American Mathematical Monthly, 120 (4): 346–354, doi:10.4169/amer...