Low-distortion embeddings of infinite metric spaces into the real line

Annals of Pure and Applied Logic 157 (2-3):148-160 (2009)

Abstract
We present a proof of a Ramsey-type theorem for infinite metric spaces due to Matoušek. Then we show that for every K>1 every uncountable Polish space has a perfect subset that K-bi-Lipschitz embeds into the real line. Finally we study decompositions of infinite separable metric spaces into subsets that, for some K>1, K-bi-Lipschitz embed into the real line
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DOI 10.1016/j.apal.2008.09.014
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A Dual Open Coloring Axiom.Stefan Geschke - 2006 - Annals of Pure and Applied Logic 140 (1):40-51.

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