Functional Limit (Topological Version)

Similar to Functional Limit we can define the definition in terms of Epsilon-Neighborhoods:

Functional Limit, Epsilon-Neighborhood Version

Let $c$ be a Limit Point of the domain $f : A \to R$ . We say that $lim_{x \to c} f (x) = L$ provided that, $\forall ε > 0$ then each $V_{ε} (L)$ , then $\exists δ > 0$ where $V_{δ} (c)$ gives that property that $\forall x \in V_{δ} (c) - {c}$ (with $x \in A$ ) it follows that $f (x) \in V_{ε} (L)$ .

This really is just the same as Functional Limit, but would be more used to talk about it with topological terms.