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Topic:
fixed point and retraction theorems
Replies:
9
Last Post:
Dec 6, 2013 8:27 AM



gui
Posts:
5
Registered:
7/28/13


fixed point and retraction theorems
Posted:
Nov 15, 2013 11:44 PM


Hi,
I was trying to figure out how to solve the following problem concerning a retraction theorem:
Let j:C>D be an inclusion of the circle into the disk. Suppose that we have two continuous maps f:D>D and g:D>D and that g satisfies goj=j. Use the retraction theorem for the disk to show that there must be a point x in the disk at which f(x)=g(x).
Supposedly, this can be proven by constructing a retraction for j by assuming there is no `fixed point' (or something like this), but I am not sure how to do this. Any general suggestion would be greatly appreciated even if they are suggestions of another way of constructing a proof to answer the question.
Thanks



