Combinatorics | Lemmas | Topology
Tucker's lemma
In mathematics, Tucker's lemma is a combinatorial analog of the Borsuk–Ulam theorem, named after Albert W. Tucker. Let T be a triangulation of the closed n-dimensional ball . Assume T is antipodally symmetric on the boundary sphere . That means that the subset of simplices of T which are in provides a triangulation of where if σ is a simplex then so is −σ.Let be a labeling of the vertices of T which is an odd function on , i.e, for every vertex .Then Tucker's lemma states that T contains a complementary edge - an edge (a 1-simplex) whose vertices are labelled by the same number but with opposite signs. (Wikipedia).
