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Every open subset of R^p is the union of countable collection of

  1. Sep 1, 2014 #1
    Every open sub set of Rp is the union of countable collection of closed sets.

    I am attaching my attempt as an image file. Please guide me on how I should move ahead. Thank you very much for your help.
     

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  2. jcsd
  3. Sep 1, 2014 #2

    micromass

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    Take an irrational number ##a## in ##G##. You can find a certain open ball ##B(a,\varepsilon)## which remains in ##G##. What can you tell about the rational numbers in that ball? In particular, if ##q\in B(a,\varepsilon)## is rational, what can you tell about the closed set in the hint?
     
  4. Sep 1, 2014 #3

    WWGD

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    This is equivalent to R^p being 2nd-countable.
     
  5. Sep 2, 2014 #4
    I think I got it. Thank you for your comments
     
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