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* Topological limits.
Limits of functions are a special case of limits of filters, which are related to categorical limits as follows.
Given a topological space X, denote F the set of filters on X, x ∈ X a point, V ( x ) ∈ F the neighborhood filter of x, A ∈ F a particular filter and the set of filters finer than A and that converge to x.
The filters F are given a small and thin category structure by adding an arrow A → B if and only if A ⊆ B.
The injection becomes a functor and the following equivalence holds:

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