Spacing in "$d=2$-dimensional"

Question

What is the correct spacing if I want to write phrases like "d=3-dimensional".

If I just write $d=1$-dimensional, the spacing around the equal-sign seems to be way too wide for me?

(Maybe also the spacing around the "-" could be a little bit too small?)

(I want to use this formulation to subtly remind the reader that the input dimension is called $d$ in this text, while telling that the current sections only deals with the 1-dimensional case.)

Example:

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\newcommand{\R}{\mathbb{R}}
\begin{document}
Define a neural network $\mathcal{NN}_\theta$ as a function from $X=\R^d$ to $Y=\R$ s.t.

\[
\mathcal{NN}_\theta (x)=\dots defintion \dots \quad\forall x\in X
\]

For the rest of the section only the the $d=1$-dimensional case is considered.
\end{document}

(PS: Probably one should also add something against hyphenation, like mentioned here: Avoid hyphenation in "2-D". It would be nice if this were already included in the answer.)

Answer 1

Building on @Mico's code, with the help of xparse, I propose a \Diml command, in which the spacing around the = sign is tighter, and the argument is input in a more natural way, as d = some value. It is of course easy to adjust the spacing to your taste.

\documentclass{article}
\usepackage{amsmath} %
\usepackage{xparse}
\newcommand{\Diml}[1]{\dimlargs{#1}}
\NewDocumentCommand{\dimlargs}{>{\SplitArgument{1}{=}}m}
{\dimlargsaux#1}
\NewDocumentCommand{\dimlargsaux}{mm}{%
 \text{$ #1\mkern2mu{=}\mkern2mu#2 $\nobreakdash-dimensional}}%

\begin{document}

$\Diml{d=1},\;\Diml{e = n }$

\end{document} 

Answer 2

Assuming you've loaded the amsmath package, I would make use of its \nobreakdash directive to make sure there's never a line break between 2- and dimensional.

\documentclass{article}
\usepackage{amsmath} % for \nobreakdash and \text macros
%% Define a macro that takes an optional argument;
%% default value of optional argument is '2'.
\newcommand\diml[1][2]{\text{$#1$\nobreakdash-dimensional}}

\begin{document}
$d=\diml$, $d=\diml[3]$, $d=\diml[n]$
\end{document}