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Find some extraordinary subset of [0,1]

  • Thread starter Maclaurin
  • Start date
  • #1
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Homework Statement


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.

Homework Equations





The Attempt at a Solution



I tried some sets, but failed.
 

Answers and Replies

  • #3
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I tried that set but it was difficult for me to modify it. Can you give me more hint?
 
  • #4
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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.
 
  • #5
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I think bd of V is not the fat Cantor set..... what should I do?
 
  • #6
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ah instead of bd of V, boundary of closure of V.
 

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