28 Notations
Differential geometry is the study of things invariant under change of notation.
| Notation | Description | Source |
| $\mathcal{H}(E;F)$, $\mathcal{R}(E;F)$ | Space of derivatives; space of remainders in an $\mathcal{HR}$-system. | Definition 26.1.1 |
| $D_{\mathcal{HR}}f(x_{0})$ | $\mathcal{HR}$-derivative of $f$ at $x_{0}$. | Definition 26.1.2 |
| $\mathcal{R}_{\sigma}^{n}(E; F)$, $\mathcal{R}_{\sigma}(E;F)$ | $\sigma$-small functions of order $n$; order 1. | Definition 26.2.1 |
| $D_{\sigma} f(x_{0})$ | $\sigma$-derivative of $f$ at $x_{0}$. | Definition 26.2.3 |
| $D_{\sigma}^{n} f$ | $n$-fold $\sigma$-derivative. | Definition 26.4.2 |
| $D_{\sigma}^{n}(U; F)$ | $n$-fold $\sigma$-differentiable functions. | Definition 26.4.3 |
| $\tilde D_{\sigma}^{n}(U; F)$ | $n$-fold $\tilde \sigma$-differentiable functions. | Definition 26.4.3 |
| $C_{\sigma}^{n}(U; F)$ | $n$-fold continuously $\sigma$-differentiable functions. | Definition 26.4.4 |
| $\tilde C_{\sigma}^{n}(U; F)$ | $n$-fold continuously $\tilde \sigma$-differentiable functions. | Definition 26.4.4 |
| $L^{(n)}_{\sigma}(E; F)$ | Codomain of derivatives. $L^{(0)}_{\sigma}(E; F) = F$, $L^{(n)}_{\sigma}(E; F) = L(E; L_{\sigma}^{(n-1)}(E; F))$, equipped with the $\sigma$-uniform topology. | Definition 26.4.1 |
| $x^{(k)}$ | Tuple of $x$ repeated $k$ times. | Theorem 26.5.2 |
| $D^{+}f(x)$ | Right derivative of $f$ at $x$. | Definition 26.3.1 |
| $\omega_{z, r}$ | Standard path of winding number 1. | Definition 27.1.3 |
| $H(U; E)$ | Space of $E$-valued holomorphic functions on $U$. | Definition 27.4.1 |
| $H(A; E)$ | Space of $E$-valued holomorphic functions near $A$. | Definition 27.4.4 |
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