information:filtering, information:extraction
In terms of nearness

At the 1908 international congress of mathematics F. Riesz introduced an alternate way defining limits and continuity in concept called "nearness". A point x is defined to be near a set A ⊆ R {\displaystyle A\subseteq \mathbb {R} } if for every r > 0 there is a point a ∈ A so that | x − a | < r. In this setting the lim x → a f (x) = L {\displaystyle \lim _{x\to a}f(x)=L} if and only if for all A ⊆ R, {\displaystyle A\subseteq \mathbb {R},} L is near f (A) whenever a is near A.Here f (A) is the set { f (x) | x ∈ A }. {\displaystyle \{f(x)|x\in A\}.} This definition can also be extended to metric and topological spaces.