Spacing around a comma to separates conditions (in math mode)

Question

Let say I have a set

\{ x \in A : first condition , second condition , third condition \},

or as a more explicit example

\{ x \in A : x > 0 , x^2 \in B , x^3 \notin C \}.

I find that the spacing around the commas are too small, and sometime it makes it hard to identify the different conditions. What would be a good practice to have nice spacing there?

I thought of \ , \. But I really does not like it, since the code is messy afterwards. An other solution I thought of is \mathbin{,} or \mathrel{,}. Does anyone has better suggestion or motivations for choosing one of these solutions over the others.

Answer 1

Related to something I wrote recently, I would use ,\  in math mode, and just “text mode” when text is involved. I put “” because by text mode I don't mean \text.

\newcommand*\mathwords{\textnormal}
$\{ x \in A : \mathwords{first condition, second condition, third condition} \}$
$\{ x \in A : x > 0 ,\ x^2 \in B ,\ x^3 \notin C \}$

Something should be done so that TeX would break between lines and hyphenate the words in \mathwords, ideally. But here it's just an example.