LaTeX-examples/tikz/topology-continuous-mapping/topology-continuous-mapping.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[->] (-0.5,0) -- (1.5,0) node [below] {$\mathbb{R}$};

    \foreach \x in {0,...,1}
        \draw (\x,0.1) -- (\x,-0.1) node [below] {\x};


    \draw[thick,red] (0.07,0.1) -- (0,0.1) -- (0,-0.1) -- (0.07,-0.1) node [below] {};
    \draw[thick,red] plot [smooth] coordinates{(0.47,0.1) (0.5,0) (0.47,-0.1)};
    \draw[thick,red] (0,0) -- (0.5,0);
    \draw[dotted,red] (0,-0.03) -- (0.5,-0.03);

    \begin{scope}[shift={(4,0)}]
        \draw[thick] (0cm,0cm) circle(1cm);
        \draw[thick, red] ([shift={(180:1cm)}]-0.0,0) arc (180:0:1cm);
        \draw[red, dotted] ([shift={(180:0.97cm)}]-0.0,0) arc (180:0:0.97cm);
        \draw (0:1cm) node[point, label=right:{$0$}] {};
    \end{scope}

    \coordinate (circleUp)       at (2.6, 0.1);
    \coordinate (circleDown)     at (2.6,-0.1);
    \coordinate (numberlineUp)   at (1.7, 0.1);
    \coordinate (numberlineDown) at (1.7,-0.1);

    \path[->] (numberlineUp)   edge  [bend left]  node[label=$f$]  {} (circleUp);
    \path[<-] (numberlineDown) edge  [bend right] node[label=below:$g$]  {} (circleDown);
\end{tikzpicture}
\end{document}