added images of simplexes

documents/GeoTopo/Kapitel2.tex

@@ -511,7 +511,7 @@ $\partial X$ ist eine Mannigfaltigkeit der Dimension $n-1$.
 
 \begin{beispiel}
     \begin{enumerate}[label=\arabic*)]
-        \item Alle endlichen Gruppen sind 0-Dimensionale Lie-Gruppen.
+        \item Alle endlichen Gruppen sind 0-dimensionale Lie-Gruppen.
         \item $\text{GL}_n(\mdr)$
         \item $(\mdr^\times, \cdot)$
         \item $(\mdr_{>0}, \cdot)$
@@ -577,7 +577,28 @@ $\partial X$ ist eine Mannigfaltigkeit der Dimension $n-1$.
     \end{enumerate}
 \end{definition}
 
-\todo[inline]{Bilder von 1, 2, 3-simplex}
+\begin{figure}[ht]
+    \centering
+    \subfloat[0-Simplex $\Delta^0$]{
+        \parbox{5cm}{\centering\input{figures/topology-simplex-0.tex}}
+        \label{fig:simplex-0}
+    }
+
+    \subfloat[1-Simplex $\Delta^1$]{
+        \input{figures/topology-simplex-1.tex}
+        \label{fig:simplex-1}
+    }%
+    \subfloat[2-Simplex $\Delta^2$]{
+        \input{figures/topology-simplex-2.tex}
+        \label{fig:simplex-2}
+    }%
+    \subfloat[3-Simplex $\Delta^3$]{
+        \input{figures/topology-simplex-3.tex}
+        \label{fig:simplex-3}
+    }%
+    \label{fig:k-simplexe}
+    \caption{Beispiele für $k$-Simplexe}
+\end{figure}
 
 % Die Übungsaufgaben sollen ganz am Ende des Kapitels sein.
 \input{Kapitel2-UB}

documents/GeoTopo/figures/topology-simplex-0.tex

@@ -0,0 +1,4 @@
+    \begin{tikzpicture}[thick]
+        \draw[thick, fill=black, black] (0cm,0cm) circle(0.1cm);
+        %\node[below] {$1$};
+    \end{tikzpicture}

documents/GeoTopo/figures/topology-simplex-1.tex

@@ -0,0 +1,25 @@
+\begin{tikzpicture}
+    \tikzstyle{point}=[thick,draw=black,cross out,inner sep=0pt,minimum width=4pt,minimum height=4pt]
+    \begin{axis}[
+        legend pos=south west,
+        axis x line=middle,
+        axis y line=middle,
+        grid = major,
+        width=5cm,
+        height=5cm,
+        grid style={dashed, gray!30},
+        xmin=0,    % start the diagram at this x-coordinate
+        xmax=3,    % end   the diagram at this x-coordinate
+        ymin=0,    % start the diagram at this y-coordinate
+        ymax=3,    % end   the diagram at this y-coordinate
+        %xlabel=$x$,
+        %ylabel=$y$,
+        tick align=outside,
+        minor tick num=-3,
+        enlargelimits=true,
+        tension=0.08]
+      \addplot[domain=0:2.5, red, thick,samples=20] {-x+2.5};
+      \node[point,label={[label distance=0cm]45:$e_0$}] at (axis cs:2.5,0) {};
+      \node[point,label={[label distance=0cm]0:$e_1$}] at (axis cs:0,2.5) {};
+    \end{axis} 
+\end{tikzpicture}

documents/GeoTopo/figures/topology-simplex-2.tex

@@ -0,0 +1,24 @@
+\begin{tikzpicture}
+    \tikzstyle{point}=[thick,draw=black,cross out,inner sep=0pt,minimum width=4pt,minimum height=4pt]
+    \begin{axis}[
+        legend pos=south west,
+        axis x line=middle,
+        axis y line=middle,
+        grid = major,
+        width=5cm,
+        height=5cm,
+        grid style={dashed, gray!30},
+        xmin=0,    % start the diagram at this x-coordinate
+        xmax=3,    % end   the diagram at this x-coordinate
+        ymin=0,    % start the diagram at this y-coordinate
+        ymax=3,    % end   the diagram at this y-coordinate
+        tick align=outside,
+        minor tick num=-3,
+        enlargelimits=true,
+        tension=0.08]
+        \node (a)[point,label={[label distance=0cm]5:$e_0$}] at (axis cs:2.5,0) {};
+        \node (b)[point,label={[label distance=0cm]5:$e_1$}] at (axis cs:0,2.5) {};
+        \node (c)[point,label={[label distance=0cm]0:$e_2$}] at (axis cs:2,2) {};
+        \draw[thick,fill=orange!50] (a.center) -- (b.center) -- (c.center) -- cycle;
+    \end{axis} 
+\end{tikzpicture}

documents/GeoTopo/figures/topology-simplex-3.tex

@@ -0,0 +1,11 @@
+\begin{tikzpicture}
+    \tikzstyle{point}=[thick,draw=black,cross out,inner sep=0pt,minimum width=4pt,minimum height=4pt]
+
+    \node (a)[point,label={[label distance=0cm]180:$e_0$}] at (0,0) {};
+    \node (b)[point,label={[label distance=0cm]0:$e_1$}] at (2,0) {};
+    \node (c)[point,label={[label distance=0cm]0:$e_2$}] at (1,2) {};
+    \node (d)[point,label={[label distance=0cm]0:$e_3$}] at (1,0.7) {};
+    \draw (a.center) -- (b.center) -- (c.center) -- cycle;
+    \draw[dashed] (a.center) -- (d.center) -- (b.center);
+    \draw[dashed] (d.center) -- (c.center);
+\end{tikzpicture}