"coincide on a set" vs "coincide in a set"

[jaakov]

Dear all:

What is correct, what sounds better:

Two maps f,g coincide on a set X if f|_X=g|_X.

Or

Two maps f,g coincide in a set X if f|_X=g|_X.

Thank you in advance
Jaakov.

[Don Phillipson]

Post by jaakov
Two maps f,g coincide on a set X if f|_X=g|_X.
Or
Two maps f,g coincide in a set X if f|_X=g|_X.

This is obviously not standard English but the jargon
(for publication) of a particular speciality: so the rules
or preferences that apply are those of this special-purpose
jargon. Those of standard English are at most secondary
to your professional purpose.