As mentioned in comments, there is no italic correction in math-mode. There may be fonts which provide a better kerning in this case and of course, you could ask the maintainer of your font to include kerning pairs for C\forall
and F\forall
.
But actually I would not recommend that as it gets difficult to read if set too close together. I would treat \forall
like a real word and therefore write something like $C\ \forall\ x$
.
If you want to have some special kerning different to your proposed \,
you might use my following MWE. Of course, you could define macros for often used combinations (\newcommand*{\Cforall}{C\,\forall}
) or define your own \forall
(\newcommand*{\myForall}{\,\forall\,}
). The last option is quite similar to what the command \in
is producing...
% arara: pdflatex
\documentclass{article}
\begin{document}
\noindent
$C\forall x$\\
$C\,\forall\,x$\\
$C\mkern4mu\forall\mkern4mu x$\\
$C\ \forall\ x$
\end{document}

$f$
is not italics. Also,\forall
is just a symbol that translates tofor all
rather than it being an operator that acts on certain operands (left and/or right). So, the spacing is ultimately up to you.\forall
is not an operator, but the F touches the\forall
that follows, which I found ugly.\forall
after a comma and a space, the space is usually a normal space\
or a\enskip
(half of an\quad
) in inline math and a full\quad
in display math. E.g.,$\forall x \in \mathbb{C}, \enskip \exists \alpha_0 > 1$
.