EDB — 0K4

[0K4] Let \((Y, σ)\) be a Hausdorff topological space. Let \((J,≤)\) be a set with filtering order (defined in [06M]↺↻). Let \(φ:J→ Y\) be a net (already met in Sec. [29X]↺↻).

We define that \(\lim _{j∈ J} φ(x) = ℓ ∈ Y\) if and only if, for every neighborhood \(V\) of \(ℓ\) in \(Y\) you have that \(φ(j)∈ V\) eventually for \(j∈ J\).