Open subset of a perfect set.

  • Thread starter kostas230
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  • #1
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Suppose we have a perfect set [itex]E\subset\mathbb{R}^k[/itex]. Is there an open set [itex]I\subset E[/itex]?
 

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  • #2
mathman
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I'm rusty at this. However, I understand that a closed interval is a perfect set. Take the closed unit cube in Rk, drop all boundary points leaving an open unit cube.
 
  • #3
Office_Shredder
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Sometime's it's true (like mathman's example), and sometimes it's false. For example the Cantor set is a perfect set but contains no open interval inside of it
 
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  • #4
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Yeah, I just found out that. Thank you :)
 

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