Spacing and brackets

Question

I know this is a duplicate but I can't find the original post. Square brackets do not display with the correct spacing around = or \cong. For example :

$[0,1[ \cong [a,b[ \hspace{5ex} ]0,1] \cong ]a,b] \hspace{5ex} ]0,1[ \cong ]a,b[$

displays

Answer 1

by default [ is a mathopen and ] is mathclose, but you can force other interpretations

\documentclass{article}
\begin{document}
$[0,1\mathclose[ \cong [a,b\mathclose[ \hspace{5ex} \mathopen]0,1] \cong 
  \mathopen]a,b] \hspace{5ex} \mathopen]0,1\mathclose[ \cong \mathopen]a,b\mathclose[$
\end{document}

In practice you would want to hide this in a suitable command eg using mathtools \DeclarePairedDelmiter :

\DeclarePairedDelmiter\oointerval][
\DeclarePairedDelmiter\ocinterval]]
\DeclarePairedDelmiter\cointerval[[
\DeclarePairedDelmiter\ccinterval[]