# Definition(s) > [!NOTE] Definition 1 (Open sets in $\mathbb{R}^n$) > $U \subset \mathbb{R}^n$ is open iff $\forall x\in U: \exists \varepsilon>0: \mathbb{B}_{\varepsilon}(x) \subset U$where $\mathbb{B}_{\varepsilon}(x)$ is the [[Open Euclidean Ball|open ball]] of radius $\varepsilon$ centred at $x.$ > [!NOTE] Definition 2 (Open Sets in $\mathbb{R}^n$ is complement of Closed set) > Let $n$ be a positive integer. Given a [[Subset|subset]] $X$ of the [[Real n-Space|real n-space]] $\mathbb{R}^n,$ we say that $X$ is open iff the [[Set Difference|set difference]] $\mathbb{R}^n\setminus X$ is [[Closed Sets|closed]]. > [!Example] Example > The trivial subsets of $\mathbb{R}^n$ are both open and closed # Properties(s) # Application(s) **More examples**: # Bibliography