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ArticleOriginal scientific text

Title

Banach spaces and bilipschitz maps

Authors 1

Affiliations

  1. Matematiikan Laitos, Helsingin Yliopisto, Hallituskatu 15, SF-00100 Helsinki, Finland

Abstract

We show that a normed space E is a Banach space if and only if there is no bilipschitz map of E onto E ∖ {0}.

Bibliography

  1. P. Tukia and J. Väisälä, Quasisymmetric embeddings of metric spaces, Ann. Acad. Sci. Fenn. Ser. A I Math. 5 (1980), 97-114.
  2. J. Väisälä, Quasimöbius maps, J. Analyse Math. 44 (1984/85), 218-234.
  3. J. Väisälä, Free quasiconformality in Banach spaces I, Ann. Acad. Sci. Fenn. Ser. A I Math. 15 (1990), 355-379.
Studia Mathematica
1992/103/3
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Pages:
291-294
Main language of publication
English
Received
1992-03-17
Published
1992
Exact and natural sciences