Updated spec config.
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This commit is contained in:
Bokuan Li
2026-03-12 22:02:52 -04:00
parent 61f66523e0
commit 68ec8c38a7
3 changed files with 4 additions and 4 deletions

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@@ -1 +1 @@
CmdLine { -n24 -n9 -n17 } CmdLine { -n24 -n9 -n17 -n25 }

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@@ -1,6 +1,6 @@
database = "spec.db" database = "spec.db"
document = "document.tex" document = "document.tex"
siteTitle = "Garden" siteTitle = "Jerry's Digital Garden"
[compiler] [compiler]
compileAll = false compileAll = false
@@ -9,7 +9,7 @@ indirectReferences = true
[website] [website]
font = "roboto" font = "roboto"
primaryColour = "blue" primaryColour = "violet"
neutralColour = "grey" neutralColour = "grey"
searchLimit = 16 searchLimit = 16
maxSearchPages = 48 maxSearchPages = 48

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@@ -40,7 +40,7 @@
Let $E, F$ be TVSs over $K \in \RC$ with $F$ being separated, $\sigma \subset B(E)$ be an upward-directed family that contains all finite sets, $U \subset E$ be open, and $f: U \to F$, then $f$ is \textbf{$\sigma$-differentiable on $U$} if it is $\sigma$-differentiable at every point in $U$. In which case, the map $D_\sigma f: U \to L(E; F)$ is the \textbf{$\sigma$-derivative} of $f$. Let $E, F$ be TVSs over $K \in \RC$ with $F$ being separated, $\sigma \subset B(E)$ be an upward-directed family that contains all finite sets, $U \subset E$ be open, and $f: U \to F$, then $f$ is \textbf{$\sigma$-differentiable on $U$} if it is $\sigma$-differentiable at every point in $U$. In which case, the map $D_\sigma f: U \to L(E; F)$ is the \textbf{$\sigma$-derivative} of $f$.
\end{definition} \end{definition}
\begin{definition}] \begin{definition}
\label{definition:derivative-garden} \label{definition:derivative-garden}
Let $E, F$ be TVSs over $K \in \RC$ with $F$ being separated, $\sigma^E_{\text{Fin}}, \sigma^E_{c}, \sigma^E_b \subset 2^E$ be the collection of all finite, compact, and bounded subsets, respectively, then differentiability with respect to $\sigma^E_{\text{Fin}}, \sigma^E_{c}, \sigma^E_b$ correspond to \textbf{Gateaux}, \textbf{Hadamard}, and \textbf{Fréchet} differentiability. Let $E, F$ be TVSs over $K \in \RC$ with $F$ being separated, $\sigma^E_{\text{Fin}}, \sigma^E_{c}, \sigma^E_b \subset 2^E$ be the collection of all finite, compact, and bounded subsets, respectively, then differentiability with respect to $\sigma^E_{\text{Fin}}, \sigma^E_{c}, \sigma^E_b$ correspond to \textbf{Gateaux}, \textbf{Hadamard}, and \textbf{Fréchet} differentiability.
\end{definition} \end{definition}