[texhax] Odd spacing around a mathbin

[Michael Barr]

Consider the file

\documentclass{article}
\begin{document}
$A\cup \lim(B)$
\end{document}

(which could as well be a plain document).  When composed and viewed, the 
\cup comes much closer to the A than to the lim.  According to the TeXbook 
(p. 170 in the 17th printing), the spacing between a mathbin and either a 
mathord or a mathop and vice versa is supposed to be the same 2mu.  I 
first noticed this on a tight line, where the \cup butted right against 
the \lim while there was still space between the A and the \cup.  Sure I 
could insert the space by hand, but I would like to know why this is so 
oddly spaced and can anything systematic be done about it?  Incidentally, 
adding italic correction has no effect.

Michael