Within this question we find the notation $\lambda f . \lambda g . \lambda x.f(g\ x)$, and that causes me to wonder about a point of LaTeX and MathJax usage.

The code `a.b.c.`

gets rendered as $a.b.c,$ with the period, or "full stop" if you like, closer to the letter to its left than the one to its right.

As one would expect, the code `a{.}b{.}c`

gives more symmetrical results: $a{.}b{.}c$.

But if we put `\newcommand{\.}{\mathbin{.}}`

$\newcommand{\.}{\mathbin{.}}$at the begining (or above the `\begin{document}`

in $\LaTeX$) then the code `a\.b\.c`

gives us $a\.b\.c,$ with an amount of horizontal space appropriate to a binary operation or binary relation symbol (e.g. the code `3+5`

will normally result in $3+5$ and not in $3{+}5$).

\begin{align} & a.b.c \\[5pt] & a{.}b{.}c \\[5pt] & a\.b\.c \end{align}

Which version should be used in this context?

`\lambda x.f`

. And anyway, just about everybody does that, so you can consider it the typographical standard. $\endgroup$Pacific Journal of Mathematics? $\endgroup$`\.`

. Journals use their own macros, and uncommon single-character macro names like this seem particularly prone to unexpected conflict. (I agree with being discomfited by treating the`.`

as punctuation when, say, the $\mapsto$ in the mathematician's version $f \mapsto g \mapsto x \mapsto f(g(x))$ is not so treated, but here I agree with @EmilJeřábek's comment that one should probably regard this as established convention nonetheless.) $\endgroup$`\.`

alreadyisa standard LaTeX command (for the text-mode dot-above diacritic), and overloading standard commands in a submission is a bad idea indeed. $\endgroup$`\!`

,`\,`

,`\`

,`\;`

, and`\:`

(and probably others), but forgot the existing meaning of`\.`

. $\endgroup$