Lipschitz extensions and Lipschitz retractions in metric spaces
Nguyen Van Khue, Nguyen To Nhu (1981)
Colloquium Mathematicae
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Nguyen Van Khue, Nguyen To Nhu (1981)
Colloquium Mathematicae
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J. Wilker (1971)
Fundamenta Mathematicae
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Robert Fraser (1970)
Fundamenta Mathematicae
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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.
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.
Jeremy T. Tyson (2005)
Fundamenta Mathematicae
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We study the bi-Lipschitz embedding problem for metric compacta hyperspaces. We observe that the compacta hyperspace K(X) of any separable, uniformly disconnected metric space X admits a bi-Lipschitz embedding in ℓ². If X is a countable compact metric space containing at most n nonisolated points, there is a Lipschitz embedding of K(X) in ; in the presence of an additional convergence condition, this embedding may be chosen to be bi-Lipschitz. By way of contrast, the hyperspace K([0,1])...
Karol Baron (1983)
Annales Polonici Mathematici
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Tadeusz Mostowski (2004)
Banach Center Publications
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Chandan S. Vora (1973)
Rendiconti del Seminario Matematico della Università di Padova
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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 . 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...
Jeff Cheeger, Bruce Kleiner, Andrea Schioppa (2016)
Analysis and Geometry in Metric Spaces
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We prove metric differentiation for differentiability spaces in the sense of Cheeger [10, 14, 27]. As corollarieswe give a new proof of one of the main results of [14], a proof that the Lip-lip constant of any Lip-lip space in the sense of Keith [27] is equal to 1, and new nonembeddability results.
Heiko Berninger, Dirk Werner (2003)
Extracta Mathematicae
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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?
Robert Fraser (1969)
Studia Mathematica
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