Closed set

• categories: Real Analysis, Definition

Definition

$E$ If contains all of it limit points

Intuition : Boundary is included in the set

Examples :

• Point $p$ in $\mathbb{R}$
• $[a,b]$ in $\mathbb{R}$

Theorem 1 : Arbitrarily intersection of closed sets is closed Theorem 2 : Finite union of closed sets is closed