From ed6f8597158b020885a841b1218c88129c34afbf Mon Sep 17 00:00:00 2001 From: Martin Thoma Date: Sat, 22 Feb 2014 09:48:53 +0100 Subject: [PATCH] =?UTF-8?q?Tippfehler=20korrigiert;=20fehlende=20Definitio?= =?UTF-8?q?n=20erg=C3=A4nzt?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- documents/GeoTopo/GeoTopo.pdf | Bin 5229713 -> 5229853 bytes documents/GeoTopo/Kapitel1.tex | 2 +- documents/GeoTopo/Kapitel3.tex | 9 +- .../GeoTopo/definitions/definitionen.pdf | Bin 361889 -> 361962 bytes documents/GeoTopo/meta/.aspell.de.pws | 399 ++++++++++++++++++ .../GeoTopo/other-formats/GeoTopo-A5.pdf | Bin 5282723 -> 5282990 bytes 6 files changed, 408 insertions(+), 2 deletions(-) create mode 100644 documents/GeoTopo/meta/.aspell.de.pws diff --git a/documents/GeoTopo/GeoTopo.pdf b/documents/GeoTopo/GeoTopo.pdf index 47153998599098beef9175c09a2680f1f0ee60cf..49f04827e00762bae225beab16ec5a30a14ce7d3 100644 GIT binary patch delta 137351 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Eine (geschlossene) \textbf{Jordankurve} in $X$ ist ein Homöomorphismus $\gamma: [0,1] \rightarrow C \subseteq X$ bzw. - $\gamma: S^1 \rightarrow C \subseteq X$. + $\gamma: S^1 \rightarrow C \subseteq X$, wobei $C := \Bild{\gamma}$. \end{definition} \begin{satz}[Jordanscher Kurvensatz] diff --git a/documents/GeoTopo/Kapitel3.tex b/documents/GeoTopo/Kapitel3.tex index 26752ba..abf8d70 100644 --- a/documents/GeoTopo/Kapitel3.tex +++ b/documents/GeoTopo/Kapitel3.tex @@ -915,7 +915,7 @@ $p|_{V_j}: V_j \rightarrow U$ Homöomorphismus. $\tilde{y_0} \in q^{-1}(x_0) \subseteq \tilde{Y}$. Nach \cref{thm:12.11} gibt es genau eine Überlagerung - \[f:\tilde{X} \rightarrow \tilde{Y} \text{ mit } f(x_0) = \tilde{Y_0} \text{ und } q \circ f = p\] + \[f:\tilde{X} \rightarrow \tilde{Y} \text{ mit } f(x_0) = \tilde{y_0} \text{ und } q \circ f = p\] und genau eine Überlagerung \[g: \tilde{Y} \rightarrow \tilde{X} \text{ mit } g(\tilde{y_0}) = \tilde{x_0} \text{ und } p \circ g = q\] @@ -931,6 +931,13 @@ $p|_{V_j}: V_j \rightarrow U$ Homöomorphismus. Die Frage, wann es eine universelle Überlagerung gibt, beantwortet der folgende Satz: +\begin{definition}\xindex{Umgebungsbasis}% + Sei $(X, \fT)$ ein topologischer Raum und $x \in X$. + + $U \subseteq \fT$ heißt eine \textbf{Umgebungsbasis} von $x$, wenn jede offene Umgebung + von $x$ eine Teilmenge von $U$ enthält. +\end{definition} + \begin{satz}%In Vorlesung: Satz 12.13 Es sei $X$ ein wegzusammenhängender topologischer Raum in dem jeder Punkt eine Umgebungsbasis aus einfach zusammenhängenden diff --git a/documents/GeoTopo/definitions/definitionen.pdf b/documents/GeoTopo/definitions/definitionen.pdf index 5f4e8f1160592fc97dcbcfd21d2992c577b99e7f..4377b54d67319947e136908626fd43fa05f30949 100644 GIT binary patch delta 36405 zcmV)HK)t`Aix%pO7O>bQ0yH<1flnxZPs{(`#P`ky# zuuz-i!NYVsoy^!^dkD<0-y^BJCACj?`vz>)z9e>!tjoE4=Q~HIi^+0QO#c3)==uNW zClvlKCUn9Iq6;%I?tf}0Ki)ri`MQ|gz~8={6ogwddGANwPndS!C49b{eEZ~oU-=xi z&=bWuk(v(80i%r~R@i!uPp+Q)^>ZpGmRQBq5`NY 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