I am currently revising a paper and I am completely confused about the commas. Is it correct English to write

1) "The canonical map $X \to Y$, $x \mapsto f(x)$, is injective."

or is it

2) "The canonical map $X \to Y$, $x \mapsto f(x)$ is injective." ,

i.e. is the second comma mandatory, optional or wrong?

  • 16
    $\begingroup$ It would be best to write "The canonical map $X\to Y$ given by $x\mapsto f(x)$ is injective". Neither 1) nor 2) sound like full sentences to my ear, and one should always avoid "(maths),(maths)"! $\endgroup$ – Mark Grant May 6 '13 at 9:39
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    $\begingroup$ I believe 1) is grammatically correct as the part between the commas can be considered a parenthesis (in the syntactic sense of the word), but I agree that it is best avoided. $\endgroup$ – Emil Jeřábek supports Monica May 6 '13 at 10:02
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    $\begingroup$ In the case in question one can just write "The canonical map $f:X\rightarrow Y$ is injective". $\endgroup$ – Andrea Mori May 6 '13 at 10:47
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    $\begingroup$ As this question seems completely unrelated to the software used to write the sentence, I removed the tag latex. $\endgroup$ – user9072 May 6 '13 at 11:07

Halmos's advice in "How to write mathematics" is never use punctuation to separate notation.


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