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If two topological spaces have the same homotopy type, how do I prove that their complements in an ambient space are homeomorphic?

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    Well my specific example was that I have a 2-complex which is homotopy equivalent to the 2 sphere. This directly implies that the its complement in the 3-sphere is the union of two open 3-balls. How do I show that this is true?2011-02-22

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