Talk:Brouwer fixed-point theorem: Difference between revisions

Revision as of 18:24, 7 February 2012

Revision as of 07:24, 6 May 2012

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"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)

:On the other hand, if the table is convex (or more generally, if the map is inside a convex subset of the country), the Brouwer's fixed-point theorem can be used to prove that there is a fixed point in the part of the map that represents the table (or the convex subset). But this is not as simple as the example currently given in the article. --[[Special:Contributions/82.130.37.20|82.130.37.20]] ([[User talk:82.130.37.20|talk]]) 18:24, 7 February 2012 (UTC)

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