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Math Help - Show that there exists no sequence of functions satisfying the following

  1. #1
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    Show that there exists no sequence of functions satisfying the following

    I found this interesting exercise on a topology book I'm reading, but I don't have a clue what to do.

    Show that there is no sequence {g_n} of continuous functions from R to R such that the sequence {(g_n)(x)} is bounded iff x is rational (where R = set of real numbers).
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    \mathbb{R} is complete. Use the Baire's theorem.


    Fernando Revilla
    Last edited by FernandoRevilla; February 9th 2011 at 02:24 AM.
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