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Looking for a counterexample
Posted:
Nov 28, 2010 3:30 PM


Hi all,
I am trying to find a counterexample for the following proposition (which is false):
Suppose that we have a sequence (f_n: K > R^q) (where K is a compact subset of some euclidean space R^n) of continuous functions and this sequence converges uniformly to a function f: K > R^q such that f is an imbedding of K. Then for n large enough, f_n is an imbedding
Does anyone know of a counterexample in which K is a compact n cell ??
Thanks in advance...
Greetings.



