Definition 26.4.3 (Space of Differentiable Functions).label Let $E, F$ be TVSs over $K \in \RC$ with $F$ being separated, $\sigma \subset \mathfrak{B}(E)$ be a covering ideal, $U \subset E$ be open, and $n \in \natp$, then $D_{\sigma}^{k}(U; F)$/$\tilde D_{\sigma}^{k}(U; F)$ is the space of $n$-fold $\sigma$/$\tilde \sigma$-differentiable functions from $U$ to $F$.