1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Open sets

  1. Nov 20, 2008 #1
    1. The problem statement, all variables and given/known data

    how do you show a set is open in R^n?

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 20, 2008 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    Depends on which course you are taking.
    In analysis you could show that for every point in the set there is some small ball completely contained inside the set.
    In topology you could work from the definition of open set, use a basis, show that the complement is closed, or even use some more elaborate theorem.

    So please be a little more specific :smile:
     
  4. Nov 20, 2008 #3
    im reading rudin's book: principles in mathematical analysis, ad we are talking about metric spaces, ie topology. so can you expand on you second approach to the problem please?
     
  5. Nov 20, 2008 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    The same way you prove almost anything: use the definition of open set. What is the definition of open set you are using?
     
  6. Nov 20, 2008 #5
    a set is open if every point in the set is an interior point. now i know that but i am having difficulty proving it.

    (every point being an interior point that is)
     
  7. Nov 20, 2008 #6

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    So the proof would start like: "Let x be any point in the set ..." and then shows that x satisfies the definition of an interior point.

    What is the definition of an interior point?
     
  8. Nov 20, 2008 #7
    then there exists a neighborhood of x such that neighborhood of x is contained in the set
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Open sets
  1. An Open Set (Replies: 16)

  2. Open sets (Replies: 1)

  3. Is this set open? (Replies: 5)

  4. Open set (Replies: 5)

  5. Open set (Replies: 4)

Loading...