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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!

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    See [Set of continuity points of a real function](http://math.stackexchange.com/questions/67620/set-of-continuity-points-of-a-real-function) and other questions linked from there.2012-05-29
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    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.2012-05-29
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    Oh It's pretty clear. Thanks2012-05-29

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