Canonical Lipschitz structures on compact Hilbert cube manifolds
Jouni Luukkainen (1985)
Commentationes Mathematicae Universitatis Carolinae
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Jouni Luukkainen (1985)
Commentationes Mathematicae Universitatis Carolinae
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Robert Fraser (1970)
Fundamenta Mathematicae
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Jiří Lhotský (2006)
Acta Universitatis Carolinae. Mathematica et Physica
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Robert Fraser (1969)
Studia Mathematica
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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?
Heiko Berninger, Dirk Werner (2003)
Extracta Mathematicae
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Marco Annoni, Emanuele Casini (2007)
Studia Mathematica
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We construct a new lipschitzian retraction from the closed unit ball of the Banach space l₁ onto its boundary, with Lipschitz constant 8.
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.
K. de Leeuw (1961)
Studia Mathematica
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