# Definition(s) > [!NOTE] Definition 1 (Closed Sets in $\mathbb{R}^n$) > Let $n$ be a positive integer. Given a [[Subsets|subset]] $X$ of the [[Real n-Space|real n-space]] $\mathbb{R}^n,$ we say that $X$ is closed iff, whenever a [[Sequences|sequence]] in $X,$ $(x_{j})_{j=1}^\infty$ [[Convergence|converges]] to $x\in \mathbb{R}^n$ then $x\in X.$ > [!Example] Example > Contents # Properties(s) # Application(s) **More examples**: # Bibliography