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Symbolverzeichnis erweitert; neue Bilder

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Martin Thoma 2013-10-27 11:16:34 +01:00
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commit 6535e529de
29 changed files with 439 additions and 26 deletions
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documents/GeoTopo/GeoTopo.pdf
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documents/GeoTopo/GeoTopo.tex
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@ -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}

61
documents/GeoTopo/Kapitel1.tex
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@ -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}

36
documents/GeoTopo/Symbolverzeichnis.tex
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@ -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 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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documents/GeoTopo/figures/neighbourhood-topology.tex
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@ -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

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documents/GeoTopo/figures/open-square.tex Normal file
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@ -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}

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documents/GeoTopo/figures/quadrat-in-kreis-in-dots.tex Normal file
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@ -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}

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documents/GeoTopo/figures/ursprungsgeraden.tex
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@ -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,

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documents/GeoTopo/figures/zariski-topology.tex Normal file
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@ -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}

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

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@ -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}

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tikz/neighbourhood-topology/neighbourhood-topology.tex
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@ -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

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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

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Compiled example
----------------
![Example](open-square.png)

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\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}

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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

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

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\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}

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@ -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

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

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\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}

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@ -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

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

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\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}