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March 10th, 2017, 09:37 AM   #1
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fixed point

Hi
I have a topological problem that bothers me.
Let D be the closed disk on the plane. Let A be the plane continuum that does not separate the plane and let A be contained in interior of D. Let f:A ->A be a continuous function and let g: D->D be also continuous function such that g|A = f.
So my question is: Does it imply that there exists x contained in interior of D such that g(x)=x?

Thank you in advance and sorry for my English.

Last edited by skipjack; March 10th, 2017 at 10:15 AM.
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