From 4d16eab7a381a8379bc139ed2744912683661bab Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Tue, 2 Mar 2021 21:25:06 +0100
Subject: add slides

---
 vorlesungen/slides/5/dimension.tex | 68 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 68 insertions(+)
 create mode 100644 vorlesungen/slides/5/dimension.tex

(limited to 'vorlesungen/slides/5/dimension.tex')

diff --git a/vorlesungen/slides/5/dimension.tex b/vorlesungen/slides/5/dimension.tex
new file mode 100644
index 0000000..ff687b3
--- /dev/null
+++ b/vorlesungen/slides/5/dimension.tex
@@ -0,0 +1,68 @@
+%
+% dimension.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\begin{frame}[t]
+\frametitle{Dimension von $\mathcal{K}^k(f)$ und $\mathcal{J}^k(f)$}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+
+\def\pfad{
+	(0,0) -- (1,0.3) -- (2,0.9) 
+	--
+	(4,2.4) -- (5,2.7) -- (6,3.3)
+	--
+	(8,3.7) -- (9,4) -- (10,4) -- (11,4) -- (12,4)
+}
+
+\fill[color=darkgreen!20] \pfad -- (12,0) -- cycle;
+\fill[color=orange!20] \pfad -- (12,6) -- (0,6) -- cycle;
+
+\fill[color=darkgreen!40] (9,0) -- (12,0) -- (12,4) -- (9,4) -- cycle;
+\fill[color=orange!40] (9,4) -- (12,4) -- (12,6) -- (9,6) -- cycle;
+
+\node[color=orange] at (10.5,5) {$\mathcal{J}(f)$};
+\node[color=darkgreen] at (10.5,2) {$\mathcal{K}(f)$};
+
+\node[color=orange] at (5.5,4.5) {$\mathcal{J}^k(f)\supset\mathcal{J}^{k+1}(f)$};
+\node[color=darkgreen] at (5.5,1.5) {$\mathcal{K}^k(f)\subset\mathcal{K}^{k+1}(f)$};
+
+\draw[line width=1.4pt] \pfad;
+
+\draw[->] (-0.1,6) -- (12.5,6) coordinate[label={$k$}];
+\draw[->] (-0.1,0) -- (12.5,0) coordinate[label={$k$}];
+\node at (-0.1,6) [left] {$n$};
+\node at (-0.1,0) [left] {$0$};
+\foreach \x in {0,1,2,4,5,6,8,9,10,11,12}{
+	\fill (\x,0) circle[radius=0.05];
+	\fill (\x,6) circle[radius=0.05];
+}
+\node at (0,0) [below] {$0$};
+\node at (1,0) [below] {$1$};
+\node at (2,0) [below] {$2$};
+
+\node at (4,0) [below] {$k-1$};
+\node at (5,0) [below] {$k$};
+\node at (6,0) [below] {$k+1$};
+
+\node at (8,0) [below] {$l-1$};
+\node at (9,0) [below] {$l$};
+\node at (10,0) [below] {$l+1$};
+\node at (11,0) [below] {$l+2$};
+\node at (12,0) [below] {$l+3$};
+
+\fill (9,4) circle[radius=0.05];
+
+\node[color=orange] at (-0.2,3) [rotate=90] {$\dim\mathcal{J}^k(f)$};
+\node[color=darkgreen] at (12.2,2) [rotate=-90] {$\dim\mathcal{K}^k(f)$};
+
+\node[color=orange] at (9,5) [rotate=-90] {$\dim\mathcal{J}(f)$};
+\node[color=darkgreen] at (9,2) [rotate=-90] {$\dim\mathcal{K}(f)$};
+
+\end{tikzpicture}
+\end{center}
+
+\end{frame}
-- 
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