open set

Def 16.4

$\varnothing$ is open

Def pg. 327

1. A subset $G$ of $\mathbb{R}$ is open set in $\mathbb{R}$ if for each $x\in G$ there exits a neighborhood $V$ of $x$ that $V\subseteq G$.
2. A subset $F$ of $\mathbb{R}$ is closed in $\mathbb{R}$ if the complement $C(F):=\mathbb{R}\backslash F$ is open in $\mathbb{R}$