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91 lines
3.9 KiB
TeX
91 lines
3.9 KiB
TeX
\twocolumn
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\chapter*{Symbolverzeichnis\markboth{Symbolverzeichnis}{Symbolverzeichnis}}
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\addcontentsline{toc}{chapter}{Symbolverzeichnis}
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% Mengenoperationen %
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\section*{Mengenoperationen}
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$A^C\;\;\;$ Komplement der Menge $A$\\
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$\mathcal{P}(M)\;\;\;$ Potenzmenge von $M$\\
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$\overline{M}\;\;\;$ Abschluss der Menge $M$\\
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$\partial M\;\;\;$ Rand der Menge $M$\\
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$M^\circ\;\;\;$ Inneres der Menge $M$\\
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$A \times B\;\;\;$ Kreuzprodukt zweier Mengen\\
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$A \subseteq B\;\;\;$ Teilmengenbeziehung\\
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$A \subsetneq B\;\;\;$ echte Teilmengenbeziehung\\
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$A \setminus B\;\;\;$ $A$ ohne $B$\\
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$A \cup B\;\;\;$ Vereinigung\\
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$A \dcup B\;\;\;$ Disjunkte Vereinigung\\
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$A \cap B\;\;\;$ Schnitt\\
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\section*{Geometrie}
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$AB\;\;\;$ Gerade durch die Punkte $A$ und $B$\\
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$\overline{AB}\;\;\;$ Strecke mit Endpunkten $A$ und $B$\\
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$\triangle ABC\;\;\;$ Dreieck mit Eckpunkten $A, B, C$\\
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% Gruppen %
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\section*{Gruppen}
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$\Homoo(X)\;\;\;$ Homöomorphismengruppe\\
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$\Iso(X)\;\;\;$ Isometriengruppe\\
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$\GL_n(K)\;\;\;$ Allgemeine lineare Gruppe\footnote{von \textit{\textbf{G}eneral \textbf{L}inear Group}}\\
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$\SL_n(K)\;\;\;$ Spezielle lineare Gruppe\\
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$\PSL_n(K)\;\;\;$ Projektive lineare Gruppe\\
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$\Perm(X)\;\;\;$ Permutationsgruppe\\
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$\Sym(X)\;\;\;$ Symmetrische Gruppe
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% Weiteres %
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\section*{Weiteres}
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$\fB\;\;\;$ Basis einer Topologie\\
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$\calS\;\;\;$ Subbasis einer Topologie\\
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$\fB_\delta(x)\;\;\;$ $\delta$-Kugel um $x$\\
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$\fT\;\;\;$ Topologie\\
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$\praum\;\;\;$ Projektiver Raum\\
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$\langle \cdot , \cdot \rangle\;\;\;$ Skalarprodukt\\
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$X /_\sim\;\;\;$ $X$ modulo $\sim$\\
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$[x]_\sim\;\;\;$ Äquivalenzklassen von $x$ bzgl. $\sim$\\
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$\| x \|\;\;\;$ Norm von $x$\\
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$| x |\;\;\;$ Betrag von $x$\\
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$S^n\;\;\;$ Sphäre\\
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$T^n\;\;\;$ Torus\\
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$f \circ g\;\;\;$ Verkettung von $f$ und $g$\\
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$[\gamma]\;\;\;$ Homotopieklasse eines Weges $\gamma$\\
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$\pi_X\;\;\;$ Projektion auf $X$\\
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$f|_U\;\;\;$ $f$ eingeschränkt auf $U$\\
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$f^{-1}(M)\;\;\;$ Urbild von $M$\\
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$\Rg(M)\;\;\;$ Rang von $M$\\
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$\chi(K)\;\;\;$ Euler-Charakteristik von $K$\\
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$\Delta^k\;\;\;$ Standard-Simplex\\
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$X \# Y\;\;\;$ Verklebung von $X$ und $Y$\\
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$\gamma_1 * \gamma_2\;\;\;$ Zusammenhängen von Wegen\\
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\onecolumn
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% Zahlenmengen %
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\section*{Zahlenmengen}
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$\mdn\;\;\;$ Natürliche Zahlen $(\Set{1, 2, 3, \dots})$\\
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$\mdz\;\;\;$ Ganze Zahlen ($\mdn \cup \Set{0, -1, -2, \dots}$)\\
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$\mdq\;\;\;$ Rationale Zahlen ($\mdz \cup \Set{\frac{1}{2}, \frac{1}{3}, \frac{2}{3}}$)\\
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$\mdr\;\;\;$ Reele Zahlen ($\mdq \cup \Set{\sqrt{2}, -\sqrt[3]{3}, \dots}$)\\
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$\mdr^+\;$ Echt positive reele Zahlen\\
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$\mdr^\times\;$ Einheitengruppe von $\mdr = \mdr \setminus \Set{0}$\\
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$\mdc\;\;\;$ Komplexe Zahlen ($\Set{a+ib|a,b \in \mdr}$)\\
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$\mdp\;\;\;$ Primzahlen ($2, 3, 5, 7, \dots$)\\
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$\mdh\;\;\;$ obere Halbebene ($\Set{z \in \mdc | \Im{z} > 0}$)\\
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$f:S^1 \hookrightarrow \mdr^2\;\;\;$ Einbettung der Kreislinie in die Ebene\\
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$\pi_1(X,x)\;\;\;$ Fundamentalgruppe im topologischen Raum $X$ um $x \in X$\\
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$\Fix(f)\;\;\;$ Menge der Fixpunkte der Abbildung $f$\\
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$\|\cdot\|_2\;\;\;$ 2-Norm; Euklidische Norm\\
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$\kappa\;\;\;$ Krümmung\\
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$\kappa_{\ts{Nor}}$
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$V(f)\;\;\;$ Nullstellenmenge von $f$\footnote{von \textit{\textbf{V}anishing Set}}
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\index{Faser|see{Urbild}}
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\index{kongruent|see{isometrisch}}
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\index{Kongruenz|see{Isometrie}}
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