Let $n\in\mathbb{N}$, let $U\subseteq \mathbb{R}^n$ be \reftext{def:open-subset-euclidean-space-2026a}{open}, let $k\in\mathbb{N}\cup\{0\}$, and let $\omega$ be a \reftext{def:differential-k-form-euclidean-open-set-2026a}{differential $k$-form} on $U$. Write $\omega$ in the coordinate expansion from \ref{thm:coordinate-expansion-differential-forms-euclidean-2026b}. We say that $\omega$ is of class $C^1$ if each coefficient function in that expansion is a \reftext{def:c1-map-euclidean-open-set-2026a}{$C^1$ map} from $U$ to $\mathbb{R}$.