Abstract:We prove an extension of the well-known combinatorial-topological lemma of E. Sperner to the case of infinite-dimensional cubes. It is obtained as a corollary to an infinitary extension of the Lebesgue Covering Dimension Theorem.
Keywords: simplex, colouring, covering dimension, point-finite, fixed point, algebraic topology
AMS Subject Classification: Primary 57N20; Secondary 55M20, 54F45