# oscillation of a function

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Hi Jussi,
>It could be better to write X \subseteq R, since often one thinks that \subset means a proper inclusion.
Well yes, it's a proper inclusion because X could be very small as it is usually included in a sequence of subsets, for instance, a filter basis. In fact this concept is useful to define limit of a function.
> Some mentioning of applications of oscillation?
>What Cauchy's criterion do you mean?
I did put an entry on this theorem. I think this is an interesting approach so I decided to include it in PM.
Cheers my dear friend,
Pedro