Talk:Lipschitz continuity
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[edit] The definition
The definition here seems to be restricted to R. Other definitions are in higher spaces than R? is this true? http://planetmath.org/encyclopedia/LipschitzCondition.htmlUser A1 06:22, 27 September 2006 (UTC)
- The definition is not restricted to R, Lipshitz functions are defineded on any metric space, in the section on metric spaces in this article. Oleg Alexandrov (talk) 15:12, 27 September 2006 (UTC)
[edit] Property of bilipschitz functions
The following text seems tautological:
- Every bilipschitz function is injective. A bilipschitz function is the same thing as a Lipschitz bijection whose inverse function is also Lipschitz.
In other words, if we define a bilipschitz function as a bijection that is Lipschitz and has a Lipschitz inverse, then it is trivially injective. Ideas? Haseldon 21:18, 9 November 2006 (UTC)
- But this is not how bilipschits functions were defined in the article. The definition was:
If there exists a 
with
then f is called bilipschitz.
Oleg Alexandrov (talk) 04:08, 10 November 2006 (UTC)
