Ramsey's theorem for colors from a metric space

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Abstract

The Ramsey theorem says that for any countably infinite undirected clique whose edges are colored by a finite number of colors, there is an infinite subclique whose edges are colored by a single color. In this note, we generalize the theorem to a situation where the colors form a compact metric space. © 2012 The Author(s).

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Bojańczyk, M., Kopczyński, E., & Toruńczyk, S. (2012). Ramsey’s theorem for colors from a metric space. Semigroup Forum, 85(1), 182–184. https://doi.org/10.1007/s00233-012-9404-4

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