Space between | and a function name is narrower than LaTeX

Space between | and a function name is narrower than LaTeX.

Enter the following two lines at MathJax demo

$|\cot$<br>
${|}\cot$

In LaTeX, the following two lines of code would produce same result: (run at texlive.net)

\documentclass{article}
\begin{document}
$|\cot$

${|}\cot$
\end{document}