Talk:Brouwer fixed-point theorem: Difference between revisions

Revision as of 09:06, 19 October 2011

Revision as of 18:07, 7 February 2012

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::Yes, I guess the corrected version is ok. Another, maybe simpler example, would be the open interval (0,1) and the function <math> f(x) = \frac{x}{2} </math>. Since

::the function doesn't have to be bijective, this should also work out. --[[Special:Contributions/84.73.188.172|84.73.188.172]] ([[User talk:84.73.188.172|talk]]) 14:28, 22 January 2011 (UTC)

== Illustrations: Ordinary map of a country ==

"Similarly: Take an ordinary map of a country, and suppose that that map is laid out on a table inside that country. There will always be a "You are Here" point on the map which represents that same point in the country." A country is not necessarily convex (can you name one that is?), which is required in the Brouwer's fixed-point theorem, so I don't see how this is an illustration of the theorem. An ordinary map is usually a [[contraction mapping]], so this can be proved using the [[Banach fixed-point theorem]] instead. --[[Special:Contributions/82.130.37.20|82.130.37.20]] ([[User talk:82.130.37.20|talk]]) 18:07, 7 February 2012 (UTC)