Let $M$ be a compact (real) manifold and let $\Omega^m_c(M)$ be the compactly supported $m$-forms on $M$. Apparently a linear map $T : \Omega^m_c(M) \to \mathbb{R}$ is continuous "in the sense of distributions" if $T(\omega_k) \to 0$ whenever $\omega_k$ is a sequence of smooth forms, all supported on a fixed compact set, such that all the derivatives of all the coefficients of the $\omega_k$ uniformly approach zero as $k \to \infty$.
Is there a more natural, less arbitrary-sounding way of describing the same topology on $\Omega^m_c(M)$?