Jtdcftul

I want to draw a diagram similar to this one:

For that I started with the following code:

begin{tikzpicture}

draw (0,0) node {$Y$};

draw (0,2) node {$X$};

draw[<-] (0,0.35) -- (0,1.65) node[left, midway] {$f$};

draw[thick] (1,0) -- (7,0);

draw[thick] (1,2) -- (7,2);

draw[thick] (1,2.5) -- (7,2.5);

draw[thick] (1,1.5) -- (7,1.5);

end{tikzpicture}

The only thing that I don't know how to do is the curvy parts. I would appreciate some indication.

The following is a pretty manual way to do this. I only did it for the first two lines, I hope you can apply it to the other occurrences. It uses the in and out keys of the to path construction:

documentclass[tikz]{standalone}



begin{document}

begin{tikzpicture}

draw (0,0) node {$Y$};

draw (0,2) node {$X$};

draw[<-] (0,0.35) -- (0,1.65) node[left, midway] {$f$};

draw[thick] (1,2.5) -- (7,2.5) coordinate(a);

draw[thick] (1,2) -- (7,2) coordinate(b);

draw[thick] (1,1.5) -- (7,1.5) coordinate(c);

draw[thick] (1,0) -- (7,0) coordinate(d);

draw[thick]

  (a) ++(.25,-.25) coordinate(ab) to[out=180,in=0] (a)

  (ab) to[out=180,in=0] (b)

  (ab) to[out=0,in=180] ++(.25,.25)

  (ab) to[out=0,in=180] ++(.25,-.25)

  ;

filldraw

  (ab) circle(.05)

  ;

end{tikzpicture}

end{document}

This uses the same in and out trick as Skillmon and puts it into a style dip, which takes as arguments the horizontal position and the depth, where the sign decides whether the dip is a dip (minus) or a bump (plus). (Let me also mention that you do not need to do something like draw[<-] (0,0.35) -- (0,1.65) node[left, midway] {$f$};. If you name the nodes, you can just do draw[<-] (Y) -- (X) node[left, midway] {$f$}; and TikZ will make sure to shorten the arrow without you having to compute the coordinates.)

documentclass[tikz,border=3.14mm]{standalone}

usetikzlibrary{positioning}

newcounter{dip}

begin{document}

begin{tikzpicture}[dip/.style args={#1/#2}{/utils/exec=stepcounter{dip},

insert path={%

coordinate (aux1) ({#1-abs(#2)},0) coordinate (aux2) ({#1+abs(#2)},0) coordinate (aux3)

(aux1) -- (aux2|-aux1) to[out=0,in=180]  

++({abs(#2)},#2) coordinate(dip-thevalue{dip}) to[out=0,in=180]  (aux3|-aux1)

}}]

begin{scope}[thick,local bounding box=dips]

 draw (1,2.5) [dip=5.5cm/-2.5mm]-- (7,2.5);

 fill (dip-1) circle[radius=2pt] node[right=3pt]{$b=1$};

 draw (1,2) [dip/.list={2.5cm/-2.5mm,5.5cm/2.5mm}] -- (7,2);

 fill (dip-2) circle[radius=2pt] node[right=3pt]{$b=1$};

 draw (1,1.5) [dip/.list={2.5cm/2.5mm,5.5cm/-5mm}]  -- (7,1.5);

 fill (dip-5) circle[radius=2pt] node[above right=0pt and 5pt]{$b=2$};

 draw (1,1) -- (7,1);

 draw (1,0.5) [dip=5.5cm/5mm]  -- (7,0.5);

end{scope}

node[left=2pt of dips.west] (X) {$X$};

draw (7,-0.5) -- (1,-0.5)  node[left=2pt] (Y) {$Y$};

draw[<-] (Y) -- (X) node[left, midway] {$f$};

foreach X in {1,2}

 {

  fill (dip-X|-Y) circle[radius=2pt];

  draw[dashed] (dip-X|-Y) -- (dip-X|-0,2.75);

 }

end{tikzpicture}

end{document}