A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
I need ideas on how to begin to prove that the only two sets that are both open and closed are R and ∅.
anonymous
 4 years ago
I need ideas on how to begin to prove that the only two sets that are both open and closed are R and ∅.

This Question is Closed

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1Here's one strategy: show that every open set in the real must be a union of open intervals. Then show that any union of open intervals is not closed unless it's R or the null set.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0You can also try to proof this by contradiction. There's a proof like that in the free book "Topology without Tears", which you'll easily find online. See the proof for proposition 3.3.3 there in the latest edition.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.