Best constants for Lipschitz embeddings of metric spaces into c0

Abstract. We answer a question of Aharoni by showing that every separable metric space can be Lipschitz 2-embedded into c0 and this result is sharp; this improves earlier estimates of Aharoni, Assouad and Pelant. We use our methods to examine the best constant for Lipschitz embeddings of the classical `p−spaces into c0 and give other applications. We prove that if a Banach space embeds almost isometrically into c0, then it embeds linearly almost isometrically into c0. We also study Lipschitz embeddings into c+0. 1