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 $\alpha \in J$ define $E_{𝛼}\stackrel{.}{=}\{x_{𝛽}:𝛽\in J,𝛽\ge 𝛼\}$ and

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