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Topic: Looking for a counterexample
Replies: 4   Last Post: Nov 29, 2010 2:30 PM

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Rodolfo Conde

Posts: 16
Registered: 3/24/10
Looking for a counterexample
Posted: Nov 28, 2010 3:30 PM
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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...


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