Open set

• categories: Real Analysis, Definition

Definition

$E$ If every point of $E$ is an interior point.

Intuition : Boundary is excluded from the set

Examples :

• $\varnothing$
• $(a,b)$ in $\mathbb{R}$

Theorem 1 : Arbitrarily union of open sets is open Theorem 2 : Finite intersection of open sets is open Theorem 3 : $X$ For $E\subset Y\subset X$ , $E$ is open in $Y\iff E=Y\cap G$ for some open $G$ in