# Definitions ###### Continuity in $\mathbb{R}^{n}$ Given a [[Function|function]] $f:U \subset \mathbb{R}^n \to \mathbb{R}^k,$ we say that $f$ is *continuous* at $p\in \mathbb{R}^{n}$ if $\forall \varepsilon, \exists \delta>0, \text{ such that } \forall x,p\in, \Vert x-p\Vert<\delta \implies \Vert f(x)-f(p)\Vert <\varepsilon$ where $\Vert \cdot \Vert$ denotes the [[p-Norms|standard Euclidean norms]] in $\mathbb{R}^n$ and $\mathbb{R}^m$ as needed. ###### Continuity in normed spaces ###### Continuity in metric spaces # Properties