As far as I know, we can define the topology of distribution (either on T or on noncompact nonempty set $\Omega$ ). I read one note and find we can also see the topology as one type of limit. Can anyone explain more about this?
For example $C^{\infty}(T)=\cap_{k} C^{k}(T)$ for more detailed reference, see this. How to define topology from a limit viewpoint? I know the another way to define topology of distribution from Rudin's Functional analysis. But I find it hard to understand this viewpoint.
I would also know more literature about analysis on T or $T^{n}$.