1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: (a) If A and B are disjoint closed sets in some

  1. Oct 26, 2011 #1
    (a) If A and B are disjoint closed sets in some ....

    1. The problem statement, all variables and given/known data

    (a) If A and B are disjoint closed sets in some metric space X, prove that they are separated.

    (b) Prove the same for disjoint open sets.

    (c) Fix p in X, ∂ >0, define A to be the set of all q in Z for which d(p,q) < ∂, define B similarly, with > in place of <. Prove that A and B are separated.

    2. Relevant equations


    Triangle inequality, definitions of open and closed sets


    3. The attempt at a solution

    Give me some hints to finishing part (c).

    screen-capture-2-25.png
     
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted