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: Basic topology proof of closed interval in R

  1. Jan 23, 2013 #1
    Let [tex] \{ [a_j, b_j]\}_{j\in J} [/tex] be a set of (possibly infinitely many closed intervals in R whose intersection cannot be expressed as a disjoint union of subsets of R. Prove that [tex] \bigcup\limits_{j \in J} {\{ [{a_j},{b_j}]\} }[/tex] is a closed interval in R.

    I dont understand how to attack this, and would appreciate an example or a push in the right direction! This is the first proof exercise I'd had in this course and I'm pretty lost.
  2. jcsd
  3. Jan 23, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper

    I think your problem statement is incomplete. Every subset of R can be expressed as a disjoint union of sets. I think the problem needs to say disjoint union of some particular kind of sets. What kind?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook