Content deleted Content added
→elemantary proof with stokes' theorem: resp to Sean (I don't watch pages or edit here much, so responses here may not be responded to immediately) |
|||
Line 56:
::There has been some little discussion on math.stackexchange [http://math.stackexchange.com/questions/194599/continuous-brouwers-fixed-point-theorem-via-stokess-theorem/194614#194614 here] about the validity of this proof. --[[User:Seaneberhard|Sean Eberhard]] ([[User talk:Seaneberhard|talk]]) 09:55, 12 September 2012 (UTC)
:::Fascinating discussion with some great insights. Nonetheless, there is an "obvious" way, at least to a topologist. Since we know the smooth maps have a fixed point and the continuous map can be approximated by smooth maps, just show the set of continuous maps with a fixed point is closed. Not hard. --[[User:C S|C S]] ([[User talk:C S|talk]]) 22:43, 8 May 2013 (UTC)
: Stokes theorem may well be derived from the Brouwer Fixed Point Theorem, so I would be wary of using it. But I am not certian of this, as I have not read the proof. --[[User:Dark Side of the Moon|Dark Side of the Moon]] 17:02, 28 August 2006 (UTC)
| |||