LaTeX-examples/tikz/number-ray-circle-topology/number-ray-circle-topology.tex

\documentclass[varwidth=true, border=2pt]{standalone}
\usepackage{amsmath,amssymb}
\usepackage{pgfplots}
\usepackage{tikz}
\usepackage{tkz-fct}
\usetikzlibrary{shapes.misc}

\begin{document}
\tikzset{
    point/.style={
        thick,
        draw=gray,
        cross out,
        inner sep=0pt,
        minimum width=4pt,
        minimum height=4pt,
    },
}
\begin{tikzpicture}
  
  \draw[->] (-1.5,0) -- (5.5,0) node [below] {$\mathbb{R}$};

  \foreach \x in {-1,...,5}
    \draw (\x,0.1) -- (\x,-0.1) node [below] {\x};

  \foreach \x in {-1,...,4} {
    \draw[red] (\x+0.6,0.01) -- (\x+0.6,-0.14) node [below] {};
    \draw[red] (\x+1.2,0.01) -- (\x+1.2,-0.14) node [below] {};
    \draw[red] (\x+0.6,-0.07) -- (\x+1.2,-0.07) node [below] {};
    }

    \begin{scope}[shift={(0,-2)}]
        \draw[thick] (0cm,0cm) circle(1cm);
        \draw[thick, red] ([shift={(216:1cm)}]-0.0,0) arc (216:-72:1cm);
        \draw (0:1cm) node[point, label={[right]{$0$}}] {};
        \path node[point, blue, label={[blue,above]{$\overline{a}$}}] (posU) at (-252:1cm) {};
        \path node[label={[red,left]{$U$}}] at (30:1cm) {};
    \end{scope}
    \draw (3.7cm,0cm) node[point, blue, label={[blue,above]{$a$}}] (posA) {};
    \draw (0.7cm,0cm) node[point, blue, label={[blue,above]{$\pi^{-1}(u)$}}] {};
    \draw[dashed, blue, thick] plot [smooth] coordinates{(posU) (0.2,-0.8) (2.5,-1) (posA)};

    \draw[blue, dashed, thick] (3.7cm,0cm) arc (0:180:1.5 and 0.5);

\end{tikzpicture}
\end{document}