Is there some standard for which spacing is to be preferred in the f: X -> Y notation for a function?

Three possibilities:

$f \colon X \to Y$
$f: X \to Y$
$f \mathpunct{:} X \to Y$

The respective outputs are shown here: enter image description here

  • Personally, I use \colon. – Bernard Aug 2 '16 at 0:49

The TeXbook, Chapter 16, p. 134:

If you want the `:' character to be treated as a punctuation mark instead of as a relation, just call it \colon:

$f:A\to B$

$f\colon A\to B$

Hence there shouldn't be :, but \colon.

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