Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Open subset of a perfect set.

  1. Sep 18, 2013 #1
    Suppose we have a perfect set [itex]E\subset\mathbb{R}^k[/itex]. Is there an open set [itex]I\subset E[/itex]?
     
  2. jcsd
  3. Sep 18, 2013 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

    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.
     
  4. Sep 18, 2013 #3

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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
     
  5. Sep 19, 2013 #4
    Yeah, I just found out that. Thank you :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Open subset of a perfect set.
  1. Open set x open set (Replies: 6)

  2. Open set (Replies: 2)

  3. Open sets and closures (Replies: 8)

  4. Open set (Replies: 19)

Loading...