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Math Help - function with different image, smae preimage

  1. #1
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    function with different image, smae preimage

    Please give an example of a function f, and two sets U_1,U_2:U_1 \subset U_2, U_1 \neq U_2 but f^{-1} (U_1)=f^{-1}(U_2)?

    Is there such a function in R^n?
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  2. #2
    MHF Contributor

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    Define f to map all of R^n to a single point. The inverse image of any set containing that point is all of R^n.
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