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I need to construct a function whose set of points of discontinuities is a given F-sigma set.

At the Follow-Up section of Wikipedia's article on the popcorn function, they give an example of such a function. I just don't see why would we need closedness of the sets in the proof. Could somebody briefly explain the proof?

Thanks

  • 9
    *Please* don't use abbreviations like "smb". The effort of a handful of keystrokes you save stands in no relationship to the effort you cause for everyone who tries to understand your post and isn't aware of the abbreviation.2011-09-28
  • 0
    Duplicate? [Set of continuity points of a real function](http://math.stackexchange.com/q/67620/set-of-continuity-points-of-a-real-function/)2011-09-28
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    Pete's answer in the linked thread should explain that fully; keep in mind that the complement of an $F_\sigma$-set is a $G_{\delta}$-set.2011-09-28

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