Geodesic
An infinitary version of Sperner's Lemma
Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 3, pp. 503-514.

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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.
Classification : 54F45, 55M20, 57N20
Keywords: simplex; colouring; covering dimension; point-finite; fixed point; algebraic topology 
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Hohti, Aarno. An infinitary version of Sperner's Lemma. Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 3, pp. 503-514. http://geodesic.mathdoc.fr/item/CMUC_2006__47_3_a12/