Displaying similar documents to “Bi-Lipschitz embeddings of hyperspaces of compact sets”

Best constants for Lipschitz embeddings of metric spaces into c₀

N. J. Kalton, G. Lancien (2008)

Fundamenta Mathematicae

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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 ℓ 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...

Products of Lipschitz-free spaces and applications

Pedro Levit Kaufmann (2015)

Studia Mathematica

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We show that, given a Banach space X, the Lipschitz-free space over X, denoted by ℱ(X), is isomorphic to ( ∑ n = 1 ∞ ℱ ( X ) ) ℓ ₁ . Some applications are presented, including a nonlinear version of Pełczyński’s decomposition method for Lipschitz-free spaces and the identification up to isomorphism between ℱ(ℝⁿ) and the Lipschitz-free space over any compact metric space which is locally bi-Lipschitz embeddable into ℝⁿ and which contains a subset that is Lipschitz equivalent to the unit ball of ℝⁿ. We also show...

Biseparating maps on generalized Lipschitz spaces

Denny H. Leung (2010)

Studia Mathematica

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Let X, Y be complete metric spaces and E, F be Banach spaces. A bijective linear operator from a space of E-valued functions on X to a space of F-valued functions on Y is said to be biseparating if f and g are disjoint if and only if Tf and Tg are disjoint. We introduce the class of generalized Lipschitz spaces, which includes as special cases the classes of Lipschitz, little Lipschitz and uniformly continuous functions. Linear biseparating maps between generalized Lipschitz spaces are...

Spaces of Lipschitz functions on metric spaces

Diethard Pallaschke, Dieter Pumplün (2015)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper the universal properties of spaces of Lipschitz functions, defined over metric spaces, are investigated.

A note on Lipschitz isomorphisms in Hilbert spaces

Dean Ives (2010)

Commentationes Mathematicae Universitatis Carolinae

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We show that the following well-known open problems on existence of Lipschitz isomorphisms between subsets of Hilbert spaces are equivalent: Are balls isomorphic to spheres? Is the whole space isomorphic to the half space?

Bi-Lipschitz Bijections of Z

Itai Benjamini, Alexander Shamov (2015)

Analysis and Geometry in Metric Spaces

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It is shown that every bi-Lipschitz bijection from Z to itself is at a bounded L1 distance from either the identity or the reflection.We then comment on the group-theoretic properties of the action of bi-Lipschitz bijections.

Bi-Lipschitz trivialization of the distance function to a stratum of a stratification

Adam Parusiński (2005)

Annales Polonici Mathematici

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Given a Lipschitz stratification 𝒳 that additionally satisfies condition (δ) of Bekka-Trotman (for instance any Lipschitz stratification of a subanalytic set), we show that for every stratum N of 𝒳 the distance function to N is locally bi-Lipschitz trivial along N. The trivialization is obtained by integration of a Lipschitz vector field.