# Definition If $f$ is an [[Types of Maps|injective]] [[Map]] of an [[open set]] $M$ of $\mathbb{R}^n$ ([[Real Coordinate Space|R^n]]) onto another [[open set]] $N$ of $\mathbb{R}^n$, it can be expressed concretely as: $ y_i = f_i(x_1, x_2, \ldots, x_n) \quad \text{or} \,\, \pmb{y} = \pmb{f}(\pmb{x})$ where $\{x_i, i = 1, \ldots, n\}$ define a point $\pmb{x}$ of $M$ and $\{y_i, i = 1, \ldots n\}$ likewise define a points $\pmb{y}$ of $N$. If the functions are all $C^k$-[[Differentials of a Map|differentiable]], then the [[Map]] is said to be $C^k$-differentiable.