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.
Robert Fraser (1970)
Fundamenta Mathematicae
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Tadeusz Mostowski (2004)
Banach Center Publications
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Nguyen Van Khue, Nguyen To Nhu (1981)
Colloquium Mathematicae
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Chandan S. Vora (1973)
Rendiconti del Seminario Matematico della Università di Padova
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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?
Jiří Lhotský (2006)
Acta Universitatis Carolinae. Mathematica et Physica
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Aleš Nekvinda, Luděk Zajíček (1988)
Časopis pro pěstování matematiky
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J. Wilker (1971)
Fundamenta 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.