Different horizontal (!) spacing of delimiters with `\left`, `\bigl`, `\Bigl`,

Question

I use \arrowvert as a middle delimiter. For example in the definition of sets, i.e. \lbrace x \arrowvert x < a \rbrace. Moreover, I try to avoid \left, \right and \middle but use the AMSmath macros \bigl, \Bigl, ... to set the size explicitly.

If I need the delimiters in "normal" size, I do not use any macro, but then I notice a different horizontal (!) spacing. Consider the case in that \left, \right and \middle can be used without effect, because all enclosed symbols have at most normal size. Then

\lbrace x \arrowvert x < a \rbrace

\left\lbrace x \middle\arrowvert x < a \right\rbrace

look the same vertically, but there is a little bit more horizontal space of both sides of the middle delimiter. Actually, the visual appearance of the latter looks more correct.

The same amount of additional space around the middle delimiter is inserted by the AMSmath keywords \big, \Big, ...

But what shall I do, if I need the normally sized delimiters but cannot use the triplet \left, \middle, \right because there is some over-sized content?

Using no macro as suggested by the AMSmath manual is no option, because then the additional space around the middle delimter is missing. Unfortunately, there does not seem to be something like a \normall, \normal, \normalr triplet that does no scaling but fits the horizontal spacing of the other macros.

Answer 1

Ah, that's a different question. Unfortunately, a math symbol can be either of class mathopen or mathclose, but not both at the same time.

But the following construction should do:

\mathclose{\arrowvert}\mathopen{}

for an equivalent to \middle\arrowvert. I tested it and on my screen it looks the same. But, since \arrowvert is of type mathord (and not mathrel, as I suspected previously), the direct use of \arrowvert also is really close in its look to \middle\arrowvert.

Answer 2

Note the exact behaviour of \middle in eTeX as spelled out in the reference (http://archiv.dante.de/projects/nts/archiv/etex-ref-prel.html#middle):

analogous to TeX's \left and \right, \middle specifies that the following delimiter is to serve both as a right and left delimiter; it will be set with spacing appropriate to a right delimiter w.r.t. the preceding atom(s), and with spacing appropriate to a left delimiter w.r.t. the succeeding atom(s).

You see, that \middle itself does not behave as a mathematical relation. You can force it to do so by adding \mathrel:

\mathrel{}\middle\arrowvert\mathrel{}

Should do what you want.