topology-kartenwechsel.tex 1.5 KB

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  1. \begin{tikzpicture}
  2. \draw (0,0) ellipse (2cm and 1cm);
  3. \begin{scope}[xshift=-2.2cm,yshift=-2.8cm]
  4. \draw[->] (0,0) -- (0,1.5);
  5. \draw[->] (0,0) -- (1.5,0);
  6. \node at (0.3,0.16) {$\mathbb{R}^n$};
  7. \end{scope}
  8. \begin{scope}[xshift=0.4cm,yshift=-2.8cm]
  9. \draw[->] (0,0) -- (0,1.5);
  10. \draw[->] (0,0) -- (1.5,0);
  11. \node at (0.3,0.16) {$\mathbb{R}^n$};
  12. \end{scope}
  13. \def\ringa{(-0.3,0) circle (0.5cm)}
  14. \def\ringb{(+0.3,0) circle (0.5cm)}
  15. \begin{scope}[even odd rule]
  16. \clip \ringa;
  17. \fill[pattern color=red,pattern=north east lines] \ringb;
  18. \end{scope}
  19. \begin{scope}[even odd rule,shift={(-0.7,-2)}]
  20. \clip \ringa;
  21. \fill[draw=red,pattern color=red,pattern=north east lines] \ringb;
  22. \end{scope}
  23. \begin{scope}[even odd rule,shift={(+0.7,-2)}]
  24. \clip \ringb;
  25. \fill[draw=red,pattern color=red,pattern=north east lines] \ringa;
  26. \end{scope}
  27. \draw \ringa;
  28. \draw \ringb;
  29. \node at (-1,0.3) {$U_i$};
  30. \node at (+1,0.3) {$U_j$};
  31. \node at (-1.9,-2) {$V_i$};
  32. \node at (+1.9,-2) {$V_j$};
  33. \node at (+2.0,0.7) {$X$};
  34. \path[->] (-0.35,0) edge [bend angle=10,bend right] node[label={[label distance=0.1cm]210:$\varphi_i$}] {} (-1,-1.5);
  35. \path[->] (+0.35,0) edge [bend angle=10,bend left] node[label={[label distance=0.1cm]-30:$\varphi_j$}] {} (+1,-1.5);
  36. \draw (-1,-2) circle (0.5cm);
  37. \draw (+1,-2) circle (0.5cm);
  38. \draw[->, red, thick] (-0.3,-2) -- (0.3,-2);
  39. \end{tikzpicture}