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!

Interior of a set

  1. Sep 13, 2012 #1
    1. The problem statement, all variables and given/known data
    Consider the excluded point topology on a set X.
    Determine Int(A) and Cl(A) for sets A containing p and for sets A not containing p.
    Excluded point topology is all the subsets of X that exclude p.
    where p is in X.
    3. The attempt at a solution
    So the interior of a set A is the union of all open sets contained in A.
    Would the interior for A be A-p , where we exclude p.
    and would the interior be A where we include p.
    Im not sure what the smallest closed set would be that contains A.
    It seem like it would just be A.
     
  2. jcsd
  3. Sep 13, 2012 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    It would be helpful to organize you answers better.

    If p∈A,
    Determine Int(A).

    Determine Cl(A).​

    If p∉A,
    Determine Int(A).

    Determine Cl(A).​
     
  4. Sep 14, 2012 #3
    for the closure of those sets, should I try a proof by contradiction.
    for the second one assume that p is not in the closure.Since p is not in A it is in the complement so it is in a closed set.
     
  5. Sep 14, 2012 #4
    Have you proven any properties for closure and interior? For example, you can show that interior of A is the largest open set contained in A and closure of A is the smallest closed set which contains A. If you can prove this, then you're almost done.
     
  6. Sep 14, 2012 #5

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Start with some basics.

    If [itex]p\in\text{A}\,,[/itex] then is set A open or is A closed?

    If [itex]p\notin\text{A}\,,[/itex] then is set A open or is A closed?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Interior of a set
  1. Interior of a Set (Replies: 1)

  2. Interior of a Set (Replies: 4)

Loading...