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Math Forum » Discussions » sci.math.* » sci.math.research

Topic: homeomorphisms of compact sets and the hausdorff distance
Replies: 7   Last Post: Nov 9, 2010 11:52 PM

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Rodolfo Conde

Posts: 16
Registered: 3/24/10
homeomorphisms of compact sets and the hausdorff distance
Posted: Oct 18, 2010 10:00 AM
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Hi everyone...

If given a compact subset A of a metric space (X,d), it is true
that given e > 0 there exists a compact subset B_e of X such that H(A,B_e) <
e (where H is the hausdorff distance).

It is true that for e > 0 sufficiently small, B_e will be homeomorphic to A
?? Does this question has a positive answer at least in the case X=euclidean
space ?? Are there some references with respect to this question ?

thanks in advance...

Best regards...

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