Correct spacing in math inside a word

Question

Sometimes math formulas become part of a word - eg:

• "d-1-dimensional" (eg d-1-dimensional sphere, d-1-dimensional hyperplane, d-k-dimensional subspace)
• "mxn-matrix" or mxn-dimensional (matrix for example)
• "d=3-dimensional" (eg: in the d=3-dimensional case...)

If I write for example $d-1$-dimensional in LaTeX, the resulting spacing

looks very bad in my point of view as it suggest to read each math symbol as a single word ("d minus one-dimensional") instead of combining them to one word "d-minus-one-dimensional".

For the specific case of Spacing in "$d=2$-dimensional", I got already a very good answer: https://tex.stackexchange.com/a/504362/128042, now I would like to generalize this question here.

I am both interested in

1. opinions what would be good typography- how the spacing should look like and
2. elegant LaTeX-code that does this spacing in a more automated way - e.g. defining a command that autmomatically removes all horizontal spaces of a given argument. So that I can call something like \mathword{d-1}{dimensional}

Answer 1

I'd avoid most of this. You gain very little in saying that

the vector space V is (m³ + n)-dimensional

versus

the vector space V has dimension m³ + n

What meaning to attribute to

a d = 3-dimensional space

is very unclear to me: the d is completely useless and confusing. Be clear and say

a space of dimension d = 3

if you want to assign a value to the letter d.

Anyway, you can do what you ask by

\newcommand{\mathprefix}[1]{${#1}$\nobreakdash\ignorespaces}

and you can say

\mathprefix{(d-1)}dimensional
\mathprefix{d=3} dimensional
\mathprefix{m\times n}dimensional

(spaces after } are optional).

With my mathematician hat on, I'd also warn that the space of m × n matrices has dimension mn (the cross denotes a cartesian product, not a multiplication).

Note. The command \nobreakdash requires amsmath.

Technical note. You can see the seemingly redundant braces in the definition of \mathprefix; they aren't. Their purpose is twofold: first, they “freeze” the spacing, not allowing it to participate to stretching or shrinking with the other spaces in the same line; second: they disallow any line break in the formula.

Answer 2

Salient points:

1. The hyphen before "dimensional" is a text, not math hyphen, brought on by using a compound adjective.

2. I choose not to set "1", "2", or "3" as a "-dimensional" precursor in math, unless it becomes part of a larger math expression.

3. "mxn" seems to me an exception to the rule, in that one does not see it used with proper math spacing.

4. Other than case 3, if I am using a mathematical precursor to the hyphen, I think clarity is best achieved by placing it in parens and using proper math spacing.

My humble recommendation:

\documentclass{article}
\begin{document}
$(d-1)$-dimensional

$m{\times}n$-dimensional

$d ={}$3-dimensional 

$(d=3)$-dimensional
\end{document}

In the 3rd line, I am assuming that d refers to a dimension, rather than an integer. On the other hand, one could use the 4th line, if one was setting the variable d to a value of 3 for "d-dimensional" space.