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

Is this contains an open set?

  1. Apr 9, 2010 #1
    On the number line R, does [-1,[tex]\infty[/tex]) contain an open set?

    because it includes -1, don't think it is an open set.
     
  2. jcsd
  3. Apr 9, 2010 #2
    It's a half open interval that you've shown. If you define a set {[tex][-1,\infty)[/tex]} then it contains at least one half open subset.
     
    Last edited: Apr 9, 2010
  4. Apr 9, 2010 #3

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Is the question: Is [tex] [-1, \infty)[/tex] an open set?

    Or is the question: Does [tex] [-1, \infty)[/tex] contain an open set?
     
  5. Apr 10, 2010 #4
    What's the difference?
     
  6. Apr 10, 2010 #5
    It is not an open set. But it contains the open set (4, 7) for example.
     
  7. Apr 10, 2010 #6
    I guess I'm not understanding the OP's question. Any non zero interval on the reals "contains" every possible combination: [a,b],(a,b),(a,b],[a,b). Any such interval has a bijective mapping to the entire set of reals, so of course the interval [-1,[tex]\infty)[/tex] "contains" open sets.

    EDIT: Perhaps I'm mistaken, but in terms of open and closed sets or subsets, I'm considering the actual membership of a given set to be dependent on the specification (choice) of that set. Therefore I could specify that every subset of C:C subset of R be closed.
     
    Last edited: Apr 10, 2010
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Is this contains an open set?
  1. Open Sets Span (Replies: 7)

Loading...