Continuous only at rational pts

Asked May 29 '12 at 06:02

Active May 29 '12 at 06:02

Viewed 84 times

Possible Duplicate:
Set of continuity points of a real function

I'm studying continuous in analysis class. I have a question. That's simple!

Is there a function that is continuous only at rational points?

I have no idea for find that. If you know, plz some hint. thanks!

edited Apr 13 '17 at 12:20

Community

asked May 29 '12 at 06:02

japee

2

See Set of continuity points of a real function and other questions linked from there. – Jonas Meyer May 29 '12 at 06:08
2

There is no such function. For any function from $\mathbb{R} \rightarrow \mathbb{R}$, the set of discontinuities form an $F_{\sigma}$ set. The set $\mathbb{R} \backslash \mathbb{Q}$ is not an $F_{\sigma}$ set. – May 29 '12 at 06:12
Oh It's pretty clear. Thanks – japee May 29 '12 at 06:24

0 Answers0