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Remove trailing spaces

Browse source 
The commands

find . -type f -name '*.md' -exec sed --in-place 's/[[:space:]]\+$//' {} \+

and

find . -type f -name '*.tex' -exec sed --in-place 's/[[:space:]]\+$//' {} \+

were used to do so.
This commit is contained in:
Martin Thoma 2015-10-14 14:25:34 +02:00
parent c578b25d2f
commit 7740f0147f
538 changed files with 3496 additions and 3496 deletions
Download patch file Download diff file Expand all files Collapse all files

14
documents/GeoTopo/figures/2d-semicubical-parabola.tex
View file

@ -18,15 +18,15 @@
tick align=outside,
%minor tick num=-3,
enlargelimits=true]
\addplot[domain=0:12, red, thick,samples=500] {1/3*x^1.5};
\addplot[domain=0:12, dotted, orange, thick,samples=500] {1*x^1.5};
\addplot[domain=0:12, dashed, blue, thick,samples=500] {2*x^1.5};
\addplot[domain=0:12, red, thick,samples=500] {1/3*x^1.5};
\addplot[domain=0:12, dotted, orange, thick,samples=500] {1*x^1.5};
\addplot[domain=0:12, dashed, blue, thick,samples=500] {2*x^1.5};
\addplot[domain=0:12, red, thick,samples=500] {-1/3*x^1.5};
\addplot[domain=0:12, dotted, orange, thick,samples=500] {-1*x^1.5};
\addplot[domain=0:12, dashed, blue, thick,samples=500] {-2*x^1.5};
\addplot[domain=0:12, red, thick,samples=500] {-1/3*x^1.5};
\addplot[domain=0:12, dotted, orange, thick,samples=500] {-1*x^1.5};
\addplot[domain=0:12, dashed, blue, thick,samples=500] {-2*x^1.5};
\addlegendentry{$a=\frac{1}{3}$}
\addlegendentry{$a=1$}
\addlegendentry{$a=2$}
\end{axis}
\end{axis}
\end{tikzpicture}

2
documents/GeoTopo/figures/3d-function-semicubical-parabola.tex
View file

@ -27,5 +27,5 @@
}
]
\addplot3[surf] {y*y-x*x*x};
\end{axis}
\end{axis}
\end{tikzpicture}

4
documents/GeoTopo/figures/coordinate-system-2.tex
View file

@ -14,13 +14,13 @@
\tkzDefLine[orthogonal=through P,/tikz/overlay](O,X) \tkzGetPoint{helper}
\tkzInterLL(O,X)(P,helper) \tkzGetPoint{xp}
\draw [decorate,decoration={brace,amplitude=4pt,mirror}]
(O) -- (xp) node [black,midway,xshift=0cm, yshift=-0.3cm]
(O) -- (xp) node [black,midway,xshift=0cm, yshift=-0.3cm]
{\footnotesize $x_P$};
\tkzDefLine[orthogonal=through P,/tikz/overlay](O,Y) \tkzGetPoint{helper}
\tkzInterLL(O,Y)(P,helper) \tkzGetPoint{yp}
\draw [decorate,decoration={brace,amplitude=4pt}]
(O) -- (yp) node [black,midway,xshift=-0.4cm]
(O) -- (yp) node [black,midway,xshift=-0.4cm]
{\footnotesize $y_P$};
\tkzDrawPolygon(O,xp,P,yp)

4
documents/GeoTopo/figures/coordinate-system-3.tex
View file

@ -10,13 +10,13 @@
\tkzDefLine[orthogonal=through P,/tikz/overlay](O,X) \tkzGetPoint{helper}
\tkzInterLL(O,X)(P,helper) \tkzGetPoint{xp}
\draw [decorate,decoration={brace,amplitude=4pt,mirror}]
(O) -- (xp) node [black,midway,xshift=0cm, yshift=-0.3cm]
(O) -- (xp) node [black,midway,xshift=0cm, yshift=-0.3cm]
{\footnotesize $x_P$};
\tkzDefLine[orthogonal=through P,/tikz/overlay](O,Y) \tkzGetPoint{helper}
\tkzInterLL(O,Y)(P,helper) \tkzGetPoint{yp}
\draw [decorate,decoration={brace,amplitude=4pt}]
(O) -- (yp) node [black,midway,xshift=-0.4cm]
(O) -- (yp) node [black,midway,xshift=-0.4cm]
{\footnotesize $y_P$};
\tkzDrawPolygon(O,xp,P,yp)

6
documents/GeoTopo/figures/cube.tex
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@ -18,9 +18,9 @@
\path[name path=trpath] (tl) -- (fr);
\path[name path=tlpath] (tr) -- (fl);
\draw[name intersections={of=brpath and rbpath}] (intersection-1)coordinate (br){};
\draw[name intersections={of=blpath and lbpath}] (intersection-1)coordinate (bl){};
\draw[name intersections={of=trpath and tlpath}] (intersection-1)coordinate (tb){};
\draw[name intersections={of=brpath and rbpath}] (intersection-1)coordinate (br){};
\draw[name intersections={of=blpath and lbpath}] (intersection-1)coordinate (bl){};
\draw[name intersections={of=trpath and tlpath}] (intersection-1)coordinate (tb){};
\shade[right color=gray!10, left color=black!50, shading angle=105] (tf) -- (bf) -- (bl) -- (tl) -- cycle;
\shade[left color=gray!10, right color=black!50, shading angle=75] (tf) -- (bf) -- (br) -- (tr) -- cycle;

2
documents/GeoTopo/figures/neighbourhood-topology-open.tex
View file

@ -63,5 +63,5 @@
\node at (axis cs:0,3) [anchor=east] {$y$};
\node at (axis cs:2,0) [anchor=north] {$x$};
\end{axis}
\end{axis}
\end{tikzpicture}

2
documents/GeoTopo/figures/neighbourhood-topology.tex
View file

@ -43,5 +43,5 @@
\node[blue] at (axis cs:0,3) [anchor=east] {$x_2$};
\node[blue] at (axis cs:2,0) [anchor=north] {$x_1$};
\end{axis}
\end{axis}
\end{tikzpicture}

2
documents/GeoTopo/figures/number-ray-circle-topology.tex
View file

@ -9,7 +9,7 @@
},
}
\begin{tikzpicture}
\draw[->] (-1.5,0) -- (5.5,0) node [below] {$\mathbb{R}$};
\foreach \x in {-1,...,5}

2
documents/GeoTopo/figures/open-square.tex
View file

@ -23,5 +23,5 @@
% Draw axis text
\node at (axis cs:-1,0.5) [anchor=east] {$\mathfrak{B}_r(0) = $};
\end{axis}
\end{axis}
\end{tikzpicture}

4
documents/GeoTopo/figures/plane-r2.tex
View file

@ -12,10 +12,10 @@
\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}

4
documents/GeoTopo/figures/pyramid.tex
View file

@ -1,7 +1,7 @@
\begin{tikzpicture}[scale=.5, z={(.707,.3)}]
\draw (2,3,2) -- (0,0,0) -- (4,0,0) -- (4,0,4) -- (2,3,2)
\draw (2,3,2) -- (0,0,0) -- (4,0,0) -- (4,0,4) -- (2,3,2)
-- (4,0,0);
\draw[color=gray, style=dashed] (2,3,2) -- (0,0,4)
\draw[color=gray, style=dashed] (2,3,2) -- (0,0,4)
-- (0,0,0);
\draw[color=gray, style=dashed] (0,0,4) -- (4,0,4);
\end{tikzpicture}

10
documents/GeoTopo/figures/sncf-metrik.tex
View file

@ -28,14 +28,14 @@
enlargelimits=true,
tension=0.08]
% plot the stirling-formulae
\addplot[domain=-4:8, red, thick,samples=500] {0.5*x};
\addplot[domain=-2:2, red, thick,samples=500] {2*x};
\addplot[domain=-4:4, red, thick,samples=500] {x};
\addplot[domain=-4:8, red, thick,samples=500] {-0.5*x};
\addplot[domain=-4:8, red, thick,samples=500] {0.5*x};
\addplot[domain=-2:2, red, thick,samples=500] {2*x};
\addplot[domain=-4:4, red, thick,samples=500] {x};
\addplot[domain=-4:8, red, thick,samples=500] {-0.5*x};
\addplot[color=red,only marks,mark=o]
plot coordinates {
(1.5,3)
(1.5,1.5)
};
\end{axis}
\end{axis}
\end{tikzpicture}

6
documents/GeoTopo/figures/topo-halbgerade.tex
View file

@ -6,7 +6,7 @@
\node (Rright) at (6,0) {};
\draw[dashed,very thick] (Pleft) -- (P);
\draw[dotted,very thick] (P) -- (R) -- (Rright);
\draw [thick,decoration={brace,mirror,raise=0.2cm},decorate] (Pleft) -- (P) node [pos=0.5,anchor=north,yshift=-0.25cm] {$PR^-$};
\draw [thick,decoration={brace,mirror,raise=0.2cm},decorate] (P) -- (R) node [pos=0.5,anchor=north,yshift=-0.25cm] {$\overline{PR}$};
\draw [thick,decoration={brace,mirror,raise=0.8cm},decorate] (P) -- (Rright) node [pos=0.5,anchor=north,yshift=-0.85cm] {$PR^+$};
\draw [thick,decoration={brace,mirror,raise=0.2cm},decorate] (Pleft) -- (P) node [pos=0.5,anchor=north,yshift=-0.25cm] {$PR^-$};
\draw [thick,decoration={brace,mirror,raise=0.2cm},decorate] (P) -- (R) node [pos=0.5,anchor=north,yshift=-0.25cm] {$\overline{PR}$};
\draw [thick,decoration={brace,mirror,raise=0.8cm},decorate] (P) -- (Rright) node [pos=0.5,anchor=north,yshift=-0.85cm] {$PR^+$};
\end{tikzpicture}

2
documents/GeoTopo/figures/topology-1.tex
View file

@ -29,5 +29,5 @@
\node at (axis cs:0.8,1.2) [anchor=-90] {$y$};
\draw (axis cs:0.8,1.2) circle[radius=0.6];
\addplot[mark=*] coordinates {(0.8,1.2)};
\end{axis}
\end{axis}
\end{tikzpicture}

2
documents/GeoTopo/figures/topology-continuous-mapping.tex
View file

@ -9,7 +9,7 @@
},
}
\begin{tikzpicture}
\draw[->] (-0.5,0) -- (1.5,0) node [below] {$\mathbb{R}$};
\foreach \x in {0,...,1}

4
documents/GeoTopo/figures/topology-metric-hausdorff.tex
View file

@ -63,7 +63,7 @@
\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)};
@ -78,5 +78,5 @@
\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{axis}
\end{tikzpicture}

2
documents/GeoTopo/figures/topology-paths-in-r2.tex
View file

@ -23,5 +23,5 @@
(0,0) (-1,1) (-2,2) (-1,3) (0, 3) (1, 4)};
\addplot[mark=none, blue, smooth cycle, thick, tension=3] coordinates {%
(0,0) (-1,1) (-2,2) (-1,3) (0, 3) (1, 4)};
\end{axis}
\end{axis}
\end{tikzpicture}

2
documents/GeoTopo/figures/topology-simplex-1.tex
View file

@ -21,5 +21,5 @@
\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{axis}
\end{tikzpicture}

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

@ -20,5 +20,5 @@
\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{axis}
\end{tikzpicture}

2
documents/GeoTopo/figures/topology-sinx.tex
View file

@ -21,6 +21,6 @@
\addplot[domain=0.0105:0.011, blue, thick,samples=20] {10};
\addlegendentry{$\{(x, \sin(\frac{1}{x})) \in X \times Y\}$}
\addlegendentry{$(-1,1) \subseteq Y$}
\end{axis}
\end{axis}
\draw[ultra thick,blue] (0,0.5) -- (0,4);
\end{tikzpicture}

2
documents/GeoTopo/figures/topology-triangle-no-simplicial-complex.tex
View file

@ -9,7 +9,7 @@
\node (e)[point] at (0,2) {};
\node (f)[point] at (4,2) {};
\end{scope}
\node (p)[point,label={[label distance=0cm]5:$P$}] at (1.5,0.5) {};
\draw[pattern=north east lines] (a.center) -- (b.center) -- (c.center) -- cycle;

2
documents/GeoTopo/figures/topology-triangle-simplicial-complex.tex
View file

@ -9,7 +9,7 @@
\node (e)[point] at (0,2) {};
\node (f)[point] at (4,2) {};
\end{scope}
\node (p)[point,label={[label distance=0cm]5:$P$}] at (1.5,0.5) {};
\draw[pattern=north east lines] (a.center) -- (p.center) -- (b.center) -- cycle;

4
documents/GeoTopo/figures/torus-invalid-triangulation-1.tex
View file

@ -14,7 +14,7 @@
\begin{scope}[decoration={
markings,
mark=at position 0.6 with {\arrow{>}}}
]
]
\draw[postaction={decorate}] (a.center) -- (b.center);
\draw[postaction={decorate}] (d.center) -- (c.center);
\end{scope}
@ -22,7 +22,7 @@
\begin{scope}[decoration={
markings,
mark=at position 0.55 with {\arrow{>>}}}
]
]
\draw[postaction={decorate}] (b.center) -- (c.center);
\draw[postaction={decorate}] (a.center) -- (d.center);
\end{scope}

4
documents/GeoTopo/figures/torus-invalid-triangulation-2.tex
View file

@ -21,7 +21,7 @@
\begin{scope}[decoration={
markings,
mark=at position 0.6 with {\arrow{>}}}
]
]
\draw[postaction={decorate}] (a.center) -- (b.center);
\draw[postaction={decorate}] (d.center) -- (c.center);
\end{scope}
@ -29,7 +29,7 @@
\begin{scope}[decoration={
markings,
mark=at position 0.55 with {\arrow{>>}}}
]
]
\draw[postaction={decorate}] (b.center) -- (c.center);
\draw[postaction={decorate}] (a.center) -- (d.center);
\end{scope}

4
documents/GeoTopo/figures/torus-triangulation-minimal.tex
View file

@ -38,7 +38,7 @@
\begin{scope}[decoration={
markings,
mark=at position 0.6 with {\arrow{>}}}
]
]
\draw[postaction={decorate}] (a.center) -- (b.center);
\draw[postaction={decorate}] (d.center) -- (c.center);
\end{scope}
@ -46,7 +46,7 @@
\begin{scope}[decoration={
markings,
mark=at position 0.55 with {\arrow{>>}}}
]
]
\draw[postaction={decorate}] (b.center) -- (c.center);
\draw[postaction={decorate}] (a.center) -- (d.center);
\end{scope}

4
documents/GeoTopo/figures/torus-triangulation.tex
View file

@ -36,7 +36,7 @@
\begin{scope}[decoration={
markings,
mark=at position 0.6 with {\arrow{>}}}
]
]
\draw[postaction={decorate}] (a.center) -- (b.center);
\draw[postaction={decorate}] (d.center) -- (c.center);
\end{scope}
@ -44,7 +44,7 @@
\begin{scope}[decoration={
markings,
mark=at position 0.55 with {\arrow{>>}}}
]
]
\draw[postaction={decorate}] (b.center) -- (c.center);
\draw[postaction={decorate}] (a.center) -- (d.center);
\end{scope}

4
documents/GeoTopo/figures/triangle-similar.tex
View file

@ -13,8 +13,8 @@
\node at ($(C')+(0,0.4)$) {$C'$};
\node at ($(B)+(0.2,-0.2)$) {$B$};
\node at ($(C)+(0.28,0.5)$) {$C$};
\tkzDrawPolygon[ultra thick,color=blue,fill=blue!20](A,B',C')
\tkzDrawPolygon[line width=0.3pt,color=red,fill=red!20](A,B,C)
\tkzDrawPolygon[ultra thick,color=blue,fill=blue!20](A,B',C')
\tkzDrawPolygon[line width=0.3pt,color=red,fill=red!20](A,B,C)
\tkzDrawPoints(A,B',C',B,C)
\tkzLabelSegment[below,red](A,B){$c$}
\tkzLabelSegment[left,red](A,C){$b$}

2
documents/GeoTopo/figures/two-perpendiculars.tex
View file

@ -18,7 +18,7 @@
\tkzDrawLines(A,B)
\tkzDrawLine[dashed,color=orange,add=0.5 and 0.2](F,P)
\tkzDrawLine[dashed,color=blue,add=0.5 and 0.2](G,P)
%
%
\tkzLabelPoint[below left](A){$A$}
\tkzLabelPoint[below left](G){$G$}
\tkzLabelPoint[above left](P){$P$}

8
documents/GeoTopo/figures/ursprungsgeraden.tex
View file

@ -18,8 +18,8 @@
enlargelimits=true,
tension=0.08]
% plot the stirling-formulae
\addplot[domain=-4:8, red, thick,samples=500] {0.5*x};
\addplot[domain=-2:2, red, thick,samples=500] {2*x};
\addplot[domain=-4:8, red, thick,samples=500] {-0.5*x};
\end{axis}
\addplot[domain=-4:8, red, thick,samples=500] {0.5*x};
\addplot[domain=-2:2, red, thick,samples=500] {2*x};
\addplot[domain=-4:8, red, thick,samples=500] {-0.5*x};
\end{axis}
\end{tikzpicture}

2
documents/GeoTopo/figures/zariski-topology.tex
View file

@ -29,5 +29,5 @@
\addplot[mark=none] coordinates {(\i,-0.2) (\i,5.2)};
}
\addplot[mark=none] coordinates {(0,2) (5,2)};
\end{axis}
\end{axis}
\end{tikzpicture}