Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Suppose $C \subset \mathbb{R}$ is of type $F_{\sigma}$. That is $C$ can be written as the union of $F_{n}$'s where each $F_{n}$'s are closed. Then can we prove that each point of $C$ is a point of discontinuity for some $f: \mathbb{R} \to \mathbb{R}$.

I refered this link on wiki : and in the follow up subsection they given this result. I would like somebody to explain it more precisely.

share|cite|improve this question
Please fix the link. – AD. Aug 28 '10 at 4:20
You need to say something more if you want an interesting problem. Maybe you want the $F_n$'s to be small in some sense? – AD. Aug 28 '10 at 4:29
@Kenny TM: Thanks for fixing the link! – anonymous Aug 28 '10 at 7:59
up vote 2 down vote accepted

I believe you're looking for something like the construction mentioned here.

share|cite|improve this answer

One can also see this article, "S.S.Kim, Amer.Math.Monthly 106 (1999), 258-259".

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.