A Note on Dichotomies for Metric Transforms
نویسنده
چکیده
We show that for every nondecreasing concave function ω : [0,∞) → [0,∞) with ω(0) = 0, either every finite metric space embeds with distortion arbitrarily close to 1 into a metric space of the form (X,ω◦d) for some metric d on X, or there exists α = α(ω) > 0 and n0 = n0(ω) ∈ N such that for all n > n0, any embedding of {0, . . . , n} ⊆ R into a metric space of the form (X,ω ◦ d) incurs distortion at least n.
منابع مشابه
Lecture Notes on Descriptive Set Theory
Metric spaces, Borel and analytic sets, Baire property and measurability, dichotomies, equivalence relations. Possible topics: determinacy, group actions, rigidity, turbulence.
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