Cfrgtkky

How to draw such a image? math and text is OK, but the horizontal and vertical lines really troubles me.

I'd recommend tikzmark for that. You have to run it three times.

documentclass[fleqn]{article}

usepackage{amsmath}

usepackage{tikz}

usetikzlibrary{tikzmark}

begin{document}

[ qquadqquadtikzmarknode[inner sep=1pt]{f}{f(x)}~tikzmarknode[inner sep=1pt]{eq}{=}~a_0

+sumlimits_{n=1}^infty left(a_n cos(n,x)+b_n cos(n,x)right)]

medskip

begin{tabular}{p{2.5cm}l}

tikzmarknode[inner sep=1pt]{b}{bounded} & tikzmarknode[inner sep=1pt]{p}{pointwise convergence}\

integrable & uniform convergence\

dots & dots \

end{tabular}

begin{tikzpicture}[overlay,remember picture]

draw ([yshift=0.5ex]f.south west) |- (f.south east) coordinate[pos=0.75] (f1)

 -- ++ (0,0.5ex);

draw ([yshift=0.5ex]eq.south west) |- (eq.south east) coordinate[pos=0.75] (eq1)

 -- ++ (0,0.5ex);

draw ([yshift=-0.5ex]b.north west) |- (b.north east) coordinate[pos=0.75] (b1)

 -- ++ (0,-0.5ex);

draw ([yshift=-0.5ex]p.north west) |- (p.north east) coordinate[pos=0.75] (p1)

 -- ++ (0,-0.5ex);

draw (f1) -- ++ (0,-1ex) |- ([yshift=1ex]b1) -- (b1);

draw (eq1) -- ++ (0,-1ex) |- ([yshift=1ex]p1) -- (p1);

end{tikzpicture}

end{document}

Or

documentclass[fleqn]{article}

usepackage{amsmath}

usepackage{tikz}

usetikzlibrary{tikzmark}

begin{document}

[ qquadqquadtikzmarknode[inner sep=1pt]{f}{f(x)}~tikzmarknode[inner sep=1pt]{eq}{=}~a_0

+sumlimits_{n=1}^infty left(a_n cos(n,x)+b_n cos(n,x)right)]

medskip

begin{tabular}{p{2.5cm}l}

tikzmarknode[inner sep=1pt]{b}{bounded} & tikzmarknode[inner sep=1pt]{p}{pointwise convergence}\

integrable & uniform convergence\

dots & dots \

end{tabular}

begin{tikzpicture}[overlay,remember picture,semithick]

draw ([yshift=0.5ex]f.south west) |- (f.south east) coordinate[pos=0.75] (f1)

 -- ++ (0,0.5ex);

draw ([yshift=0.5ex]f.south-|eq.west) |- (f.south-|eq.east) coordinate[pos=0.75] (eq1)

 -- ++ (0,0.5ex);

draw ([yshift=-0.5ex]b.north west) |- (b.north east) coordinate[pos=0.75] (b1)

 -- ++ (0,-0.5ex);

draw ([yshift=-0.5ex]p.north west) |- (p.north east) coordinate[pos=0.75] (p1)

 -- ++ (0,-0.5ex);

draw (f1) -- ++ (0,-1ex) |- ([yshift=1ex]b1) -- (b1);

draw (eq1) -- ++ (0,-1ex) |- ([yshift=1ex]p1) -- (p1);

end{tikzpicture}

end{document}

With great help of remember picture:

documentclass{article}

usepackage{tikz}

usetikzlibrary{calc,positioning}

begin{document}

[tikz[baseline,remember picture]

 node[inner xsep=0pt,minimum height=.6cm,anchor=base] (f) {$f(x)$};;

tikz[baseline,remember picture]

 node[inner xsep=0pt,minimum height=.6cm,anchor=base] (e)

 {$=$vphantom{$f(x)$}};;a_0+sum_{n=1}^infty a_ncos(nx)+b_nsin(nx)]



begin{tikzpicture}[overlay,remember picture]

draw (f.south west)|-($(f.south east)+(0,-.1)$)--(f.south east);

draw ($(f.south)+(0,-.1)$)--++(0,-.3)-|++(-1,-.3) node[below,align=left] 

{bounded\integrable\continuous\differentiable\$f'$ continuous};

draw (e.south west)|-($(e.south east)+(0,-.1)$)--(e.south east);

draw ($(e.south)+(0,-.1)$)--++(0,-.3)-|++(1,-.3) 

node[below right=0pt and -5ex,align=left] 

{pointwise convergence\uniform convergence\$L^2$ convergence\Cesaro mean convergence};

end{tikzpicture}

end{document}

However, due to the option overlay, the TikZ picture doesn't work really well with normal documents.

A tricky solution is to put vspace{}:

documentclass{article}

usepackage{tikz}

usetikzlibrary{calc,positioning}

usepackage{lipsum}

begin{document}

lipsum[1]

[tikz[baseline,remember picture]

 node[inner xsep=0pt,minimum height=.6cm,anchor=base] (f) {$f(x)$};;

tikz[baseline,remember picture]

 node[inner xsep=0pt,minimum height=.6cm,anchor=base] (e)

 {$=$vphantom{$f(x)$}};;a_0+sum_{n=1}^infty a_ncos(nx)+b_nsin(nx)]



begin{tikzpicture}[overlay,remember picture]

draw (f.south west)|-($(f.south east)+(0,-.1)$)--(f.south east);

draw ($(f.south)+(0,-.1)$)--++(0,-.3)-|++(-1,-.3) node[below,align=left] 

{bounded\integrable\continuous\differentiable\$f'$ continuous};

draw (e.south west)|-($(e.south east)+(0,-.1)$)--(e.south east);

draw ($(e.south)+(0,-.1)$)--++(0,-.3)-|++(1,-.3) 

node[below right=0pt and -5ex,align=left] 

{pointwise convergence\uniform convergence\$L^2$ convergence\Cesaro mean convergence};

end{tikzpicture}

vspace{6baselineskip}



lipsum[2]

end{document}

Any suggestions are welcome.