Symbolverzeichnis erweitert; neue Bilder

documents/GeoTopo/GeoTopo.tex

@@ -8,6 +8,8 @@
 \usepackage{makeidx} % for automatically generation of an index
 \usepackage[bookmarks,bookmarksnumbered,hypertexnames=false,pdfpagelayout=OneColumn,colorlinks,hyperindex=false]{hyperref} % has to be after makeidx
 \usepackage[xindy,toc,nonumberlist]{glossaries} % for symbol table, has to be after hyperref
+\usepackage{glossary-mcols}
+%\glossarystyle{mcolindex} % two column design for glossary
 \usepackage{enumerate}
 \usepackage{braket} % needed for \Set
 \usepackage{csquotes}

documents/GeoTopo/Kapitel1.tex

@@ -137,27 +137,34 @@ Auch gibt es Mengen, die sowohl abgeschlossen als auch offen sind.
     Umgebungen $U_i$ um $x_i$  mit $i=1,2$ gibt, sodass $U_1 \times U_2 \subseteq U$
     gilt.
 
-    \begin{figure}[htp]
-        \centering
-        \input{figures/neighbourhood-topology}
-        \caption{Zu $x=(x_1, x_2)$ gibt es Umgebungen $U_1, U_2$ mit $U_1 \times U_2 \subseteq U$}
-    \end{figure}
-
     $\fT = \Set{U \subseteq X_1 \times X_2 | U \text{ offen}}$
     ist eine Topologie auf $X_1 \times X_2$. Sie heißt \textbf{Produkttopologie}.
     $\fB = \Set{U_1 \times U_2 | U_i \text{ offen in } X_i, i=1,2}$
     ist eine Basis von $\fT$.
 \end{definition}
 
+\begin{figure}[htp]
+    \centering
+    \input{figures/neighbourhood-topology}
+    \caption{Zu $x=(x_1, x_2)$ gibt es Umgebungen $U_1, U_2$ mit $U_1 \times U_2 \subseteq U$}
+\end{figure}
+
 \begin{beispiel}
     \begin{enumerate}[1)]
-        \item $X_1 = X_2 = \mdr$ mit euklidischer Topologie.
-        \item $X_1 = X_2 = \mdr$ mit Zariski-Topologie.
-              $\fT$ Produkttopologie auf $\mdr^2$: $U_1 \times U_2$
+        \item $X_1 = X_2 = \mdr$ mit euklidischer Topologie.\\
               $\Rightarrow$ Die Produkttopologie auf $\mdr \times \mdr = \mdr^2$
-              stimmt mit der euklidischen Topologie auf $\mdr^2$ überein.\\
-              \todo{Bild einfügen}
+              stimmt mit der euklidischen Topologie auf $\mdr^2$ überein.
+        \item $X_1 = X_2 = \mdr$ mit Zariski-Topologie.
+              $\fT$ Produkttopologie auf $\mdr^2$: $U_1 \times U_2$\\
+              (Siehe Abb. \ref{fig:zariski-topologie})
     \end{enumerate}
+
+    \begin{figure}[htp]
+        \centering
+        \input{figures/zariski-topology}
+        \caption{Zariski-Topologie auf $\mdr^2$}
+        \label{fig:zariski-topologie}
+    \end{figure}
 \end{beispiel}
 
 \begin{definition} \xindex{Quotiententopologie}
@@ -188,8 +195,7 @@ Auch gibt es Mengen, die sowohl abgeschlossen als auch offen sind.
             &\gdw x \text{ und } y \text{ liegen auf der gleichen Ursprungsgerade}
     \end{align*}
     \[\overline{X} = \mathbb{P}^n(\mdr)\]
-    Also für $n=1$:
-
+    Also für $n=1$:\nopagebreak\\
     \input{figures/ursprungsgeraden}
 \end{beispiel}
 
@@ -215,33 +221,44 @@ Auch gibt es Mengen, die sowohl abgeschlossen als auch offen sind.
 
 \begin{beispiel}
     Sei $V$ ein euklidischer oder hermiteischer Vektorraum mit Skalarprodukt
-    $\langle \cdot \rangle$.
+    $\langle \cdot , \cdot \rangle$.
     Dann wird $V$ durch $d(x,y) := \sqrt{\langle x-y, x-y \rangle}$ zum metrischen Raum.
 \end{beispiel}
 
 \begin{beispiel}[diskrete Metrik] \xindex{Metrik!diskrete} \xindex{Topologie!diskrete}
     Sei $X$ eine Menge. Dann heißt
     \[d(x,y) = \begin{cases}
-    0: & \text{, falls } x=y\\
-    1: & \text{, falls } x \neq y
+    0 & \text{falls } x=y\\
+    1 & \text{falls } x \neq y
     \end{cases}\]
     die \textbf{diskrete Metrik}. Die Metrik $d$ induziert die 
     \textbf{diskrete Topologie}.
 \end{beispiel}
 
 \begin{beispiel}
-    $X = \mdr^2$ und $d\left ((x_1, y_1), (x_2, y_2)\right ) := \max{\|x_1 - x_2\|, \|y_1 - y_2\|}$
+    $X = \mdr^2$ und $d\left ((x_1, y_1), (x_2, y_2)\right ) := \max(\|x_1 - x_2\|, \|y_1 - y_2\|)$
     ist Metrik.
 
-    \todo[inline]{Bild von $\fB_r(0)$ erstellen und einfügen (Quadrat der Seitenlänge $2r$)}
-
     \emph{Beobachtung:} $d$ erzeugt die eukldische Topologie.
 
-    \todo[inline]{Bild von Quadrat in Kreis in Quadrat ... erstellen und einfügen.}
+    \begin{figure}[ht]
+        \centering
+        \subfigure[$\fB_r(0)$]{
+            \input{figures/open-square}
+            \label{fig:open-square}
+        }%
+        \subfigure[Euklidische Topologie]{
+            \input{figures/quadrat-in-kreis-in-dots}
+            \label{fig:quadrat-in-kreis-in-dots}
+        }%
+        \label{Formen}
+        \caption{Veranschaulichungen zur Metrik $d$}
+    \end{figure}
+
 \end{beispiel}
 
-\begin{beispiel}[SNCF-Metrik] \xindex{Metrik!SNCF}
-    $X = \mdr^2$ \footnote{Diese Metrik wird auch \enquote{\href{https://de.wikipedia.org/wiki/Franz\%C3\%B6sische_Eisenbahnmetrik}{französische Eisenbahnmetrik}} genannt.}
+\begin{beispiel}[SNCF-Metrik\footnote{Diese Metrik wird auch \enquote{\href{https://de.wikipedia.org/wiki/Franz\%C3\%B6sische_Eisenbahnmetrik}{französische Eisenbahnmetrik}} genannt.}] \xindex{Metrik!SNCF}
+    $X = \mdr^2$ 
 
     \input{figures/sncf-metrik}
 \end{beispiel}

documents/GeoTopo/Symbolverzeichnis.tex

@@ -11,6 +11,13 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % Mengenoperationen                                                 %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newglossaryentry{Potenzmenge}
+{
+  name={\ensuremath{\mathcal{P}(M)}},
+  description={Potenzmenge von $M$},
+  sort=MengenoperationNPotenzmenge
+}
+
 \newglossaryentry{Abschluss}
 {
   name={\ensuremath{\overline{M}}},
@@ -90,6 +97,35 @@
   sort=KoerperREinheiten
 }
 
+\newglossaryentry{Projektion}
+{
+  name={\ensuremath{\mathbb{P}}},
+  description={Projektion},
+  sort=KoerperXProjektion
+}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Sonstiges                                                         %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newglossaryentry{Skalarprodukt}
+{
+  name={\ensuremath{\langle \cdot , \cdot \rangle}},
+  description={Skalarprodukt},
+  sort=ZZZSkalarprodukt
+}
+
+\newglossaryentry{Norm}
+{
+  name={\ensuremath{\| x \|}},
+  description={Norm von $x$},
+  sort=ZZZNorm
+}
+
+\newglossaryentry{Betrag}
+{
+  name={\ensuremath{| x |}},
+  description={Betrag von $x$},
+  sort=ZZZNormBetrag
+}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % Fraktale Symbole                                                  %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

documents/GeoTopo/figures/neighbourhood-topology.tex

@@ -17,7 +17,7 @@
             \draw [decorate,decoration={brace,mirror,raise=12pt}] (axis cs:1.5,0) -- (axis cs:2.5,0) node [midway,below=16pt] {$U_1$};
         }]
 
-        \addplot[mark=none, orange, smooth, thick, fill=orange!30] coordinates {(1,1) (2,0.5) (3,1.5) (3,2) (3.5,3) (3.2, 5) (2.2, 4.7) (1.5, 4.2) (1.1, 3.9) (0.9, 2.5) (1,1)};
+        \addplot[mark=none, orange, smooth cycle, thick, fill=orange!30] coordinates {(1,1) (2,0.5) (3,1.5) (3,2) (3.5,3) (3.2, 5) (2.2, 4.7) (1.5, 4.2) (1.1, 3.9) (0.9, 2.5)};
         \node[orange] at (axis cs:4,4) [anchor=south] {$U$};
 
         % Draw help lines

documents/GeoTopo/figures/open-square.tex

@@ -0,0 +1,27 @@
+\begin{tikzpicture}
+    \begin{axis}[
+        axis x line=middle,
+        axis y line=middle,
+        xmin=-1.5,     % start the diagram at this x-coordinate
+        xmax= 1.5,    % end   the diagram at this x-coordinate
+        ymin=-1.5,     % start the diagram at this y-coordinate
+        ymax= 1.5,   % end   the diagram at this y-coordinate
+        ticks=none,
+        enlargelimits=true,
+        after end axis/.code={
+            \draw [decorate,decoration={brace,mirror,raise=2pt}] (axis cs:0,1) -- (axis cs:-1,1) node [midway,above=5pt] {$r$};
+            \draw [decorate,decoration={brace,mirror,raise=2pt}] (axis cs:1,1) -- (axis cs:0,1) node [midway,above=5pt] {$r$};
+            \draw [decorate,decoration={brace,mirror,raise=2pt}] (axis cs:1,0) -- (axis cs:1,1) node [midway,right=5pt] {$r$};
+            \draw [decorate,decoration={brace,mirror,raise=2pt}] (axis cs:1,-1) -- (axis cs:1,0) node [midway,right=5pt] {$r$};
+        }]
+
+
+        % Draw solid square
+        \addplot[mark=none, thick] coordinates {(-1,-1) (1,-1) (1,1) (-1,1) (-1,-1)};
+        \addplot[mark=*] coordinates {(0,0)};
+
+        % Draw axis text
+        \node at (axis cs:-1,0.5) [anchor=east] {$\mathfrak{B}_r(0) = $};
+
+    \end{axis} 
+\end{tikzpicture}

documents/GeoTopo/figures/quadrat-in-kreis-in-dots.tex

@@ -0,0 +1,9 @@
+\begin{tikzpicture}[thick]
+    \draw (-1,-1) -- (1,-1) -- (1,1) -- (-1,1) -- cycle;
+    \draw (0cm,0cm) circle(0.9cm);
+
+    \begin{scope}[scale=1.7]
+        \draw (-1,-1) -- (1,-1) -- (1,1) -- (-1,1) -- cycle;
+        \draw (0cm,0cm) circle(0.9cm);
+    \end{scope}
+\end{tikzpicture}

documents/GeoTopo/figures/ursprungsgeraden.tex

@@ -1,6 +1,6 @@
 \begin{tikzpicture}
     \begin{axis}[
-    legend pos=south east,
+        legend pos=south east,
         axis x line=middle,
         axis y line=middle,
         %grid = major,

documents/GeoTopo/figures/zariski-topology.tex

@@ -0,0 +1,33 @@
+\begin{tikzpicture}
+    \begin{axis}[
+        axis x line=middle,
+        axis y line=middle,
+        grid = major,
+        grid style={dashed, gray!30},
+        xmin= 0,     % start the diagram at this x-coordinate
+        xmax= 5,    % end   the diagram at this x-coordinate
+        ymin= 0,     % start the diagram at this y-coordinate
+        ymax= 5,   % end   the diagram at this y-coordinate
+        xtick={-1,0,1,2,3,4,5},
+        ytick={-1,0,1,2,3,4,5},
+        xlabel={$U_1 = \mathbb{R} \setminus \mathbb{N}$},
+        xlabel style={xshift=-2.5cm,yshift=-0.7cm},
+        ylabel={$U_2 = \mathbb{R} \setminus \mathbb{N}$},
+        ylabel style={rotate=-90, xshift=1.5cm},
+        xticklabels={,,},
+        yticklabels={,,},
+        tick align=outside,
+        enlargelimits=true]
+
+
+        % Draw solid square
+        \addplot[mark=o] coordinates {(0,0) (1,0) (2,0) (3,0) (4,0) (5,0)};
+        \addplot[mark=o] coordinates {(0,0) (0,1) (0,2) (0,3) (0,4) (0,5)};
+
+        \foreach \i in {0,1,2,3,4,5} {
+            \addplot[mark=none] coordinates {(-0.2,\i) (5.2,\i)};
+            \addplot[mark=none] coordinates {(\i,-0.2) (\i,5.2)};
+        }
+        \addplot[mark=none] coordinates {(0,2) (5,2)};
+    \end{axis} 
+\end{tikzpicture}

documents/steuergesetz/Makefile

@@ -0,0 +1,7 @@
+SOURCE = steuergesetz
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.out

documents/steuergesetz/steuergesetz.tex

@@ -0,0 +1,30 @@
+\documentclass[a4paper,9pt]{scrartcl}
+\usepackage{amssymb, amsmath} % needed for math
+\usepackage[utf8]{inputenc} % this is needed for umlauts
+\usepackage[ngerman]{babel} % this is needed for umlauts
+\usepackage[T1]{fontenc}    % this is needed for correct output of umlauts in pdf
+\usepackage[margin=2.5cm]{geometry} %layout
+\usepackage{hyperref}   % links im text
+\usepackage{enumerate}  % for advanced numbering of lists
+
+\hypersetup{ 
+  pdfauthor   = {Martin Thoma}, 
+  pdfkeywords = {Steuergesetzbuch}, 
+  pdftitle    = {Steuergesetzbuch} 
+} 
+
+\setcounter{secnumdepth}{5}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Begin document                                                    %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{document}
+\section{Abadsfasdf}
+adfasdfasdfasdf
+\subsection{Badsfadf}
+asdfasdfasd
+\subsubsection{Cdfadf}
+asdfasdf
+\paragraph{asdfasdf}
+asdfasdfasf
+\end{document}

tikz/neighbourhood-topology/neighbourhood-topology.tex

@@ -3,7 +3,7 @@
 \usepackage{pgfplots}
 
 \begin{document}
-\begin{tikzpicture}[>=stealth,]
+\begin{tikzpicture}
     \begin{axis}[
         axis x line=middle,
         axis y line=middle,
@@ -22,7 +22,7 @@
             \draw [decorate,decoration={brace,mirror,raise=12pt}] (axis cs:1.5,0) -- (axis cs:2.5,0) node [midway,below=16pt] {$U_1$};
         }]
 
-        \addplot[mark=none, orange, smooth, thick, fill=orange!30] coordinates {(1,1) (2,0.5) (3,1.5) (3,2) (3.5,3) (3.2, 5) (2.2, 4.7) (1.5, 4.2) (1.1, 3.9) (0.9, 2.5) (1,1)};
+        \addplot[mark=none, orange, smooth cycle, thick, fill=orange!30] coordinates {(1,1) (2,0.5) (3,1.5) (3,2) (3.5,3) (3.2, 5) (2.2, 4.7) (1.5, 4.2) (1.1, 3.9) (0.9, 2.5)};
         \node[orange] at (axis cs:4,4) [anchor=south] {$U$};
 
         % Draw help lines

tikz/open-square/Makefile

@@ -0,0 +1,31 @@
+SOURCE = open-square
+DELAY = 80
+DENSITY = 300
+WIDTH = 512
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
+
+gif:
+	pdfcrop $(SOURCE).pdf
+	convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
+	make clean
+
+png:
+	make
+	make svg
+	inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
+
+transparentGif:
+	convert $(SOURCE).pdf -transparent white result.gif
+	make clean
+
+svg:
+	#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
+	pdf2svg $(SOURCE).pdf $(SOURCE).svg
+	# Necessary, as pdf2svg does not always create valid svgs:
+	inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg

tikz/open-square/Readme.md

@@ -0,0 +1,3 @@
+Compiled example
+----------------
+![Example](open-square.png)

tikz/open-square/open-square.tex

@@ -0,0 +1,34 @@
+\documentclass[varwidth=true, border=2pt]{standalone}
+\usepackage{tikz}
+\usepackage{pgfplots}
+\usepackage{amsmath,amssymb}
+
+\begin{document}
+\begin{tikzpicture}
+    \begin{axis}[
+        axis x line=middle,
+        axis y line=middle,
+        xmin=-1.5,     % start the diagram at this x-coordinate
+        xmax= 1.5,    % end   the diagram at this x-coordinate
+        ymin=-1.5,     % start the diagram at this y-coordinate
+        ymax= 1.5,   % end   the diagram at this y-coordinate
+        ticks=none,
+        enlargelimits=true,
+        after end axis/.code={
+            \draw [decorate,decoration={brace,mirror,raise=2pt}] (axis cs:0,1) -- (axis cs:-1,1) node [midway,above=5pt] {$r$};
+            \draw [decorate,decoration={brace,mirror,raise=2pt}] (axis cs:1,1) -- (axis cs:0,1) node [midway,above=5pt] {$r$};
+            \draw [decorate,decoration={brace,mirror,raise=2pt}] (axis cs:1,0) -- (axis cs:1,1) node [midway,right=5pt] {$r$};
+            \draw [decorate,decoration={brace,mirror,raise=2pt}] (axis cs:1,-1) -- (axis cs:1,0) node [midway,right=5pt] {$r$};
+        }]
+
+
+        % Draw solid square
+        \addplot[mark=none, thick] coordinates {(-1,-1) (1,-1) (1,1) (-1,1) (-1,-1)};
+        \addplot[mark=*] coordinates {(0,0)};
+
+        % Draw axis text
+        \node at (axis cs:-1,0.5) [anchor=east] {$\mathfrak{B}_r(0) = $};
+
+    \end{axis} 
+\end{tikzpicture}
+\end{document}

tikz/plane-r2/Makefile

@@ -0,0 +1,31 @@
+SOURCE = plane-r2
+DELAY = 80
+DENSITY = 300
+WIDTH = 512
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
+
+gif:
+	pdfcrop $(SOURCE).pdf
+	convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
+	make clean
+
+png:
+	make
+	make svg
+	inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
+
+transparentGif:
+	convert $(SOURCE).pdf -transparent white result.gif
+	make clean
+
+svg:
+	#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
+	pdf2svg $(SOURCE).pdf $(SOURCE).svg
+	# Necessary, as pdf2svg does not always create valid svgs:
+	inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg

tikz/plane-r2/Readme.md

@@ -0,0 +1,3 @@
+Compiled example
+----------------
+![Example](plane-r2.png)

tikz/plane-r2/plane-r2.tex

@@ -0,0 +1,27 @@
+\documentclass[varwidth=true, border=2pt]{standalone}
+\usepackage{tikz}
+\usepackage{tikz-3dplot}
+
+\begin{document}
+\tdplotsetmaincoords{110}{50}
+\begin{tikzpicture}
+		[tdplot_main_coords,
+			cube/.style={very thick,black},
+			grid/.style={very thin,gray},
+			axis/.style={->,blue,thick}]
+
+	%draw a grid in the x-y plane
+	\foreach \x in {-0.5,0,...,2.5}
+		\foreach \y in {-0.5,0,...,2.5}
+		{
+			\draw[grid] (\x,-0.5) -- (\x,2.5);
+			\draw[grid] (-0.5,\y) -- (2.5,\y);
+		}
+			
+
+	%draw the axes
+	\draw[axis] (-1,0,0) -- (3,0,0) node[anchor=west]{$y$};
+	\draw[axis] (0,-1,0) -- (0,3,0) node[anchor=west]{$x$};
+	
+\end{tikzpicture}
+\end{document}

tikz/quadrat-in-kreis-in-dots/Makefile

@@ -0,0 +1,31 @@
+SOURCE = quadrat-in-kreis-in-dots
+DELAY = 80
+DENSITY = 300
+WIDTH = 512
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
+
+gif:
+	pdfcrop $(SOURCE).pdf
+	convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
+	make clean
+
+png:
+	make
+	make svg
+	inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
+
+transparentGif:
+	convert $(SOURCE).pdf -transparent white result.gif
+	make clean
+
+svg:
+	#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
+	pdf2svg $(SOURCE).pdf $(SOURCE).svg
+	# Necessary, as pdf2svg does not always create valid svgs:
+	inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg

tikz/quadrat-in-kreis-in-dots/Readme.md

@@ -0,0 +1,3 @@
+Compiled example
+----------------
+![Example](quadrat-in-kreis-in-dots.png)

tikz/quadrat-in-kreis-in-dots/quadrat-in-kreis-in-dots.tex

@@ -0,0 +1,15 @@
+\documentclass[varwidth=true, border=2pt]{standalone}
+\usepackage{tikz}
+\usepackage{pgfplots}
+
+\begin{document}
+\begin{tikzpicture}[thick]
+    \draw (-1,-1) -- (1,-1) -- (1,1) -- (-1,1) -- cycle;
+    \draw (0cm,0cm) circle(0.9cm);
+
+    \begin{scope}[scale=1.7]
+        \draw (-1,-1) -- (1,-1) -- (1,1) -- (-1,1) -- cycle;
+        \draw (0cm,0cm) circle(0.9cm);
+    \end{scope}
+\end{tikzpicture}
+\end{document}

tikz/zariski-topology/Makefile

@@ -0,0 +1,31 @@
+SOURCE = zariski-topology
+DELAY = 80
+DENSITY = 300
+WIDTH = 512
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
+
+gif:
+	pdfcrop $(SOURCE).pdf
+	convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
+	make clean
+
+png:
+	make
+	make svg
+	inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
+
+transparentGif:
+	convert $(SOURCE).pdf -transparent white result.gif
+	make clean
+
+svg:
+	#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
+	pdf2svg $(SOURCE).pdf $(SOURCE).svg
+	# Necessary, as pdf2svg does not always create valid svgs:
+	inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg

tikz/zariski-topology/Readme.md

@@ -0,0 +1,3 @@
+Compiled example
+----------------
+![Example](zariski-topology.png)

tikz/zariski-topology/zariski-topology.tex

@@ -0,0 +1,40 @@
+\documentclass[varwidth=true, border=2pt]{standalone}
+\usepackage{tikz}
+\usepackage{pgfplots}
+\usepackage{amsmath,amssymb}
+
+\begin{document}
+\begin{tikzpicture}
+    \begin{axis}[
+        axis x line=middle,
+        axis y line=middle,
+        grid = major,
+        grid style={dashed, gray!30},
+        xmin= 0,     % start the diagram at this x-coordinate
+        xmax= 5,    % end   the diagram at this x-coordinate
+        ymin= 0,     % start the diagram at this y-coordinate
+        ymax= 5,   % end   the diagram at this y-coordinate
+        xtick={-1,0,1,2,3,4,5},
+        ytick={-1,0,1,2,3,4,5},
+        xlabel={$U_1 = \mathbb{R} \setminus \mathbb{N}$},
+        xlabel style={xshift=-2.5cm,yshift=-0.7cm},
+        ylabel={$U_2 = \mathbb{R} \setminus \mathbb{N}$},
+        ylabel style={rotate=-90, xshift=1.5cm},
+        xticklabels={,,},
+        yticklabels={,,},
+        tick align=outside,
+        enlargelimits=true]
+
+
+        % Draw solid square
+        \addplot[mark=o] coordinates {(0,0) (1,0) (2,0) (3,0) (4,0) (5,0)};
+        \addplot[mark=o] coordinates {(0,0) (0,1) (0,2) (0,3) (0,4) (0,5)};
+
+        \foreach \i in {0,1,2,3,4,5} {
+            \addplot[mark=none] coordinates {(-0.2,\i) (5.2,\i)};
+            \addplot[mark=none] coordinates {(\i,-0.2) (\i,5.2)};
+        }
+        \addplot[mark=none] coordinates {(0,2) (5,2)};
+    \end{axis} 
+\end{tikzpicture}
+\end{document}