LaTeX-examples/documents/GeoTopo/Symbolverzeichnis.tex

\chapter*{Symbolverzeichnis}
\addcontentsline{toc}{chapter}{Symbolverzeichnis}
\begin{minipage}[t]{0.45\textwidth}
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% Mengenoperationen                                                 %
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\section*{Mengenoperationen}
$A^C\;\;\;$ Komplement der Menge $A$\\
$\mathcal{P}(M)\;\;\;$ Potenzmenge von $M$\\
$\overline{M}\;\;\;$ Abschluss der Menge $M$\\
$\partial M\;\;\;$ Rand der Menge $M$\\
$M^\circ\;\;\;$ Inneres der Menge $M$\\
$A \times B\;\;\;$ Kreuzprodukt zweier Mengen\\
$A \subseteq B\;\;\;$ Teilmengenbeziehung\\
$A \subsetneq B\;\;\;$ echte Teilmengenbeziehung\\
$A \setminus B\;\;\;$ $A$ ohne $B$\\
$A \cup B\;\;\;$ Vereinigung\\
$A \dcup B\;\;\;$ Disjunkte Vereinigung\\
$A \cap B\;\;\;$ Schnitt\\
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% Zahlenmengen                                                      %
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\section*{Zahlenmengen}
$\mdn\;\;\;$ Natürliche Zahlen $(\Set{1, 2, 3, \dots})$\\
$\mdz\;\;\;$ Ganze Zahlen ($\mdn \cup \Set{0, -1, -2, \dots}$)\\
$\mdq\;\;\;$ Rationale Zahlen ($\mdz \cup \Set{\frac{1}{2}, \frac{1}{3}, \frac{2}{3}}$)\\
$\mdr\;\;\;$ Reele Zahlen ($\mdq \cup \Set{\sqrt{2}, -\sqrt[3]{3}, \dots}$)\\
$\mdr^+\;$ Echt positive reele Zahlen\\
$\mdr^\times\;$ Einheitengruppe von $\mdr$ ($\mdr \setminus \Set{0}$)\\
$\mdc\;\;\;$ Komplexe Zahlen ($\Set{a+ib|a,b \in \mdr}$)\\
$\mdp\;\;\;$ Primzahlen ($2, 3, 5, 7, \dots$)\\

\section*{Geometrie}
$AB\;\;\;$ Gerade durch die Punkte $A$ und $B$\\
$\overline{AB}\;\;\;$ Strecke mit Endpunkten $A$ und $B$\\
$\triangle ABC\;\;\;$ Dreieck mit Eckpunkten $A, B, C$\\
\end{minipage}
\begin{minipage}[t]{0.45\textwidth}
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% Gruppen                                                           %
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\section*{Gruppen}
$\Homoo(X)\;\;\;$ Homöomorphismengruppe\\
$\Iso(X)\;\;\;$ Isometriengruppe\\
$\GL_n(K)\;\;\;$ Allgemeine lineare Gruppe (general linear group)\\
$\Perm(X)\;\;\;$ Permutationsgruppe\\
$\Sym(X)\;\;\;$ Symmetrische Gruppe
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% Weiteres                                                          %
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\section*{Weiteres}
$\fB\;\;\;$ Basis einer Topologie\\
$\fB_\delta(x)\;\;\;$ $\delta$-Kugel um $x$\\
$\fT\;\;\;$ Topologie\\

$\praum\;\;\;$ Projektiver Raum\\
$\langle \cdot , \cdot \rangle\;\;\;$ Skalarprodukt\\
$X /_\sim\;\;\;$ $X$ modulo $\sim$\\
$[x]_\sim\;\;\;$ Äquivalenzklassen von $x$ bzgl. $\sim$\\
$\| x \|\;\;\;$ Norm von $x$\\
$| x |\;\;\;$ Betrag von $x$\\

$S^n\;\;\;$ Sphäre\\
$T^n\;\;\;$ Torus\\

$[\gamma]\;\;\;$ Homotopieklasse eines Weges $\gamma$\\
$\pi_X\;\;\;$ Projektion auf $X$\\
$f|_U\;\;\;$ $f$ eingeschränkt auf $U$\\
$f^{-1}(M)\;\;\;$ Urbild von $M$\\
$\text{Rg}(M)\;\;\;$ Rang von $M$\\
$\chi(K)\;\;\;$ Euler-Charakteristik von $K$\\
$\Delta^k\;\;\;$ Standard-Simplex\\
$X \# Y\;\;\;$ Verklebung von $X$ und $Y$\\
$\gamma_1 * \gamma_2\;\;\;$ Zusammenhängen von Wegen\\
\end{minipage}

$f:S^1 \hookrightarrow \mdr^2\;\;\;$ Einbettung der Kreislinie in die Ebene\\
$\pi_1(X,x)\;\;\;$ Fundamentalgruppe im topologischen Raum $X$ um $x \in X$\\
$\Fix(f)\;\;\;$ Menge der Fixpunkte der Abbildung $f$

\index{Faser|see{Urbild}}