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zSymCh@ZniD5pUBP9xJa_MuvoXMYp$JuR=$S$bBO?R*vt@Pvmph}9*HYu1t6*3vp~!<0WDlHf95)bi?!-v^Rq z5ob4rB^psP_DBpEgUFbN8X^yYlhd^sV(g5nX7w8f-9kwcA5SiR#TW`|gO1W$__gVM zr2OiWld&SpkgL_C2*%pL5s%E3vI6;-V;PWLG_jk0d(`+AX|DDRKb7l{TXo_`4ymQF z;bW=Aw9NAXF3M$!QevkW7PSaHdeAV$gDf+#<2(3yT81oJ{G`TQtXBLyVyc1T5qVs9bvf4`-t%K!iX diff --git a/documents/GeoTopo/Kapitel2.tex b/documents/GeoTopo/Kapitel2.tex index 6e7f86f..a7f8bdb 100644 --- a/documents/GeoTopo/Kapitel2.tex +++ b/documents/GeoTopo/Kapitel2.tex @@ -251,14 +251,12 @@ $\partial X$ ist eine Mannigfaltigkeit der Dimension $n-1$. Sei $X$ eine $n$-dimensionale Mannigfaltigkeit mit Atlas $(U_i, \varphi_i)_{i \in I}$ - \begin{enumerate}[label=\alph*)] - \item Für $i, j \in I$ mit $U_i, U_j \neq \emptyset$ heißt + Für $i, j \in I$ mit $U_i, U_j \neq \emptyset$ heißt \begin{align*} \varphi_{ij} &:= \varphi_j \circ \varphi_i^{-1}\\ \varphi_i (U_i \cap U_j) &\rightarrow \varphi_j (U_i \cap U_j) \end{align*} \textbf{Kartenwechsel} oder \textbf{Übergangsfunktion}. - \end{enumerate} \end{definition} \begin{figure}[htp] @@ -361,7 +359,7 @@ $\partial X$ ist eine Mannigfaltigkeit der Dimension $n-1$. \begin{definition} $S \subseteq \mdr^3$ heißt \textbf{reguläre Fläche}\xindex{Fläche!reguläre} $:\gdw$ - $\forall s \in S\;\exists $ Umgebung $V \subseteq \mdr^3$ $\exists U \subseteq \mdr^2$ offen: $\exists$ differenzierbare Abbildung + $\forall s \in S\;\exists $ Umgebung $V(s) \subseteq \mdr^3$ $\exists U \subseteq \mdr^2$ offen: $\exists$ differenzierbare Abbildung $F: U \rightarrow V \cap S$: $\text{Rg}(J_F(u)) = 2\;\;\;\forall u \in U$. $F$ heißt (lokale) reguläre Parametrisierung von $S$.