Re: Scattered sets are G-delta

Hi, physicist's view:

1) your scattered set S should be countable (because every compact interval <-K;K> of R can contain only finite number of isolated points); you can intersect S with <-K;K> and take isolated points until there are some
2) now when S is countable collection of isolated points x_n, for every n there is eps_n such that (x_n-eps_n;x_n+eps_n) intersects S only at point x_n; for every natural m define G_m as union over n of open sets (x_n-eps_n/m,x_n+eps_n/m). For every m you get open set and intersection of all of G_m gives S.

I don't know if it is correct, but I hope it can help you somehow.

Tomas
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