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 ?