profile-img
Sahil posted an Question
April 16, 2020 • 21:58 pm 30 points
  • CSIR NET
  • Mathematical Sciences

Arbitrary collection of disjoint open intervals is countable.will same be true for arbitrary collection of disjoint closed intervals...

arbitrary collection of disjoint open intervals is countable.will same be true for arbitrary collection of disjoint closed intervals...

1 Answer(s) Answer Now
  • 0 Likes
  • 7 Comments
  • 0 Shares
  • comment-profile-img>
    Chandra prakash

    Let U be an open set in R. Then U is a countable union of disjoint intervals. This question has probably been asked. However, I am not interested in just getting the answer to it. Rather, I am interested in collecting as many different proofs of it which are as diverse as possible. A professor told me that there are many. So, I invite everyone who has seen proofs of this fact to share them with the community. I think it is a result worth knowing how to prove in many different ways and having a post that combines as many of them as possible will, no doubt, be quite useful. After two days, I will place a bounty on this question to attract as many people as possible. Of course, any comments, corrections, suggestions, links to papers/notes etc. are more than welcome.

whatsapp-btn

Do You Want Better RANK in Your Exam?

Start Your Preparations with Eduncle’s FREE Study Material

  • Updated Syllabus, Paper Pattern & Full Exam Details
  • Sample Theory of Most Important Topic
  • Model Test Paper with Detailed Solutions
  • Last 5 Years Question Papers & Answers