EDB — 2B7

[2B7]Prerequisites:[06P]↺↻,[230]↺↻.Difficulty:**.

Let \((Y,\sigma )\) be a Hausdorff topological space. Let \(J\) be a filtering set and \( x:J\to Y\) be a net in \(Y\). For every \(α ∈ J\) define \(E_{𝛼}{\stackrel{.}{=}}\{ x_{𝛽} : 𝛽 ∈ J, 𝛽 ≥ 𝛼 \} \) and

Prove that \(E\) coincides with the set \(L\) of limit points (defined in [2B4]↺↻).