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}.
@article{bwmeta1.element.bwnjournal-article-smv103i3p291bwm, author = {J. V\"ais\"al\"a}, title = {Banach spaces and bilipschitz maps}, journal = {Studia Mathematica}, volume = {103}, year = {1992}, pages = {291-294}, zbl = {0814.46013}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv103i3p291bwm} }
Väisälä, J. Banach spaces and bilipschitz maps. Studia Mathematica, Tome 103 (1992) pp. 291-294. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv103i3p291bwm/
[00000] [1] P. Tukia and J. Väisälä, Quasisymmetric embeddings of metric spaces, Ann. Acad. Sci. Fenn. Ser. A I Math. 5 (1980), 97-114. | Zbl 0403.54005
[00001] [2] J. Väisälä, Quasimöbius maps, J. Analyse Math. 44 (1984/85), 218-234. | Zbl 0593.30022
[00002] [3] J. Väisälä, Free quasiconformality in Banach spaces I, Ann. Acad. Sci. Fenn. Ser. A I Math. 15 (1990), 355-379. | Zbl 0696.30022