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Theorem of perturbation of the identity
Posted:
Feb 12, 2013 7:49 PM


I'm having troubles with the last statement of this question:
Let ?:A?R be a contraction defined in an open set A?R. Prove the map f:A?R, defined by f(x)=x+?(x) is a homeomorphism from A to an open set f(A)?R. Besides that, if A=R, then f(A)=R.
I need help with f(A)=R. How can I prove that?
Thanks a lot



