Hausdorff-Topology

tikz/topology-metric-hausdorff/Makefile

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+SOURCE = topology-metric-hausdorff
+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/topology-metric-hausdorff/Readme.md

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+Compiled example
+----------------
+![Example](topology-metric-hausdorff.png)

tikz/topology-metric-hausdorff/topology-metric-hausdorff.tex

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+\documentclass[varwidth=true, border=2pt]{standalone}
+
+\usepackage{pgfplots}
+\usepackage{tikz}
+\usetikzlibrary{patterns}
+
+% defining the new dimensions and parameters
+\newlength{\hatchspread}
+\newlength{\hatchthickness}
+\newlength{\hatchshift}
+\newcommand{\hatchcolor}{}
+% declaring the keys in tikz
+\tikzset{hatchspread/.code={\setlength{\hatchspread}{#1}},
+         hatchthickness/.code={\setlength{\hatchthickness}{#1}},
+         hatchshift/.code={\setlength{\hatchshift}{#1}},% must be >= 0
+         hatchcolor/.code={\renewcommand{\hatchcolor}{#1}}}
+% setting the default values
+\tikzset{hatchspread=6pt,
+         hatchthickness=0.4pt,
+         hatchshift=0pt,% must be >= 0
+         hatchcolor=black}
+% declaring the pattern
+\pgfdeclarepatternformonly[\hatchspread,\hatchthickness,\hatchshift,\hatchcolor]% variables
+   {custom north west lines}% name
+   {\pgfqpoint{\dimexpr-2\hatchthickness}{\dimexpr-2\hatchthickness}}% lower left corner
+   {\pgfqpoint{\dimexpr\hatchspread+2\hatchthickness}{\dimexpr\hatchspread+2\hatchthickness}}% upper right corner
+   {\pgfqpoint{\dimexpr\hatchspread}{\dimexpr\hatchspread}}% tile size
+   {% shape description
+    \pgfsetlinewidth{\hatchthickness}
+    \pgfpathmoveto{\pgfqpoint{0pt}{\dimexpr\hatchspread+\hatchshift}}
+    \pgfpathlineto{\pgfqpoint{\dimexpr\hatchspread+0.15pt+\hatchshift}{-0.15pt}}
+    \ifdim \hatchshift > 0pt
+      \pgfpathmoveto{\pgfqpoint{0pt}{\hatchshift}}
+      \pgfpathlineto{\pgfqpoint{\dimexpr0.15pt+\hatchshift}{-0.15pt}}
+    \fi
+    \pgfsetstrokecolor{\hatchcolor}
+%    \pgfsetdash{{1pt}{1pt}}{0pt}% dashing cannot work correctly in all situation this way
+    \pgfusepath{stroke}
+   }
+
+\begin{document}
+\begin{tikzpicture}
+    \begin{axis}[
+        legend pos=south west,
+        axis x line=middle,
+        axis y line=middle,
+        %grid = major,
+        %width=9cm,
+        %height=4.5cm,
+        grid style={dashed, gray!30},
+        xmin=-1,     % start the diagram at this x-coordinate
+        xmax= 6,    % end   the diagram at this x-coordinate
+        ymin=-0.25,     % start the diagram at this y-coordinate
+        ymax= 5,   % end   the diagram at this y-coordinate
+        axis background/.style={fill=white},
+        xlabel=$X_1$,
+        ylabel=$X_2$,
+        %xticklabels={,,},
+        %yticklabels={,,},
+        %xtick={-1,0,1,2,3,4,5},
+        %ytick={-1,0,1,2,3,4,5},
+        ticks=none,
+        %tick align=outside,
+        enlargelimits=true,
+        tension=0.08]
+        \addplot[hatchcolor=red,mark=none, pattern=custom north west lines, draw=none] coordinates {(0.5, 0) (0.5,5) (1.5,5) (1.5,0) };
+        \addplot[red,mark=none, thick] coordinates {(0.5, 0) (0.5,5)};
+        \addplot[red,mark=none, thick] coordinates {(1.5, 0) (1.5,5)};
+
+        \addplot[hatchcolor=red,mark=none, pattern=custom north west lines, draw=none] coordinates {(4.5, 0) (4.5,5) (5.5,5) (5.5,0) };
+        \addplot[red,mark=none, thick] coordinates {(4.5, 0) (4.5,5)};
+        \addplot[red,mark=none, thick] coordinates {(5.5, 0) (5.5,5)};
+ 
+
+        \addplot[mark=none, dashed] coordinates {(1, 0) (1,3)};
+        \addplot[mark=none, dashed] coordinates {(5, 0) (5,3)};
+
+        \addplot[mark=x] coordinates {(1, 3)};
+        \addplot[mark=x] coordinates {(5, 3)};
+        \node at (axis cs:1,3) [anchor=north west] {$(x_1, y_1)$};
+        \node at (axis cs:5,3) [anchor=north west] {$(x_2, y_2)$};
+
+        \node at (axis cs:1,0) [anchor=north] {$x_1$};
+        \node at (axis cs:5,0) [anchor=north] {$x_2$};
+
+        \node[red] at (axis cs:1,-0.3) [anchor=north] {$U_1 \times X_2$};
+        \node[red] at (axis cs:5,-0.3) [anchor=north] {$U_2 \times X_2$};
+    \end{axis} 
+\end{tikzpicture}
+\end{document}