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Find some extraordinary subset of [0,1]

  1. Nov 17, 2011 #1
    1. The problem statement, all variables and given/known data
    I want to find a subset A of [0,1] such that A=cl(int A) and bd A does not have measure zero where cl means closure and int means interior.

    2. Relevant equations



    3. The attempt at a solution

    I tried some sets, but failed.
     
  2. jcsd
  3. Nov 17, 2011 #2

    micromass

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  4. Nov 17, 2011 #3
    I tried that set but it was difficult for me to modify it. Can you give me more hint?
     
  5. Nov 17, 2011 #4

    micromass

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    Well, you want the fat Cantor set to be the boundary of the set you want.

    Every step you leave out some open intervals. Now let V be the union of the open intervals you leave out at the odd steps. Take [itex]\overline{V}[/itex] to be your set.
     
  6. Nov 18, 2011 #5
    I think bd of V is not the fat Cantor set..... what should I do?
     
  7. Nov 18, 2011 #6
    ah instead of bd of V, boundary of closure of V.
     
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