EDB — 0K4

[0K4] Let $(Y,\sigma )$ be a Hausdorff topological space. Let $(J,\le )$ be a set with filtering order (defined in [06M]↺↻). Let $\phi :J\to Y$ be a net (already met in Sec. [29X]↺↻).

We define that $\underset{j\in J}{lim}\phi (x)=\ell \in Y$ if and only if, for every neighborhood $V$ of $\ell$ in $Y$ you have that $\phi (j)\in V$ eventually for $j\in J$.