A smooth function is a function that is infinitely differentiable. The space of smooth functions defined on \(U\subseteq \mathbb{R}^d\) is
\begin{equation*} C^{\infty}(U)=\bigcap_{k=1}^{\infty} C^k(U). \end{equation*}A smooth function is a function that is infinitely differentiable. The space of smooth functions defined on \(U\subseteq \mathbb{R}^d\) is
\begin{equation*} C^{\infty}(U)=\bigcap_{k=1}^{\infty} C^k(U). \end{equation*}