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is a function with no fixed point. But if we set <math>x = \frac{1}{2}</math> and <math>y = \sqrt{\frac{3}{4}}</math>,
then <math> f(x,y) = (x,y) </math>.--[[Special:Contributions/84.73.188.172|84.73.188.172]] ([[User talk:84.73.188.172|talk]]) 18:07, 19 January 2011 (UTC)
:Congratulations! You found an error that has been in the article since [http://en.wikipedia.org/w/index.php?title=Brouwer_fixed_point_theorem&action=historysubmit&diff=57654312&oldid=46581414 June 2006]!
:The idea is valid, though. I will replace the example with a hopefully correct one using the homeomorphism of the interval (-π/2,π/2) with the real line via the tan and arctan functions. Since I have just made this up and did not put much thought into it, it would be nice if you could check it. [[User:Hans Adler|Hans]] [[User talk:Hans Adler|Adler]] 20:46, 19 January 2011 (UTC)
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