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    Prepositions under vs with respect to

    Please tell me what preposition must be used after the word "close" in the following phrase pertaining to the
    mathematical analysis:

    category is closed under morphisms


    category is closed with respect to morphisms

    or both are correct.


  1. Raymott's Avatar
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    "closed under morphism" appears 700 times in Google; the other term zero times. (That's not a definitive answer).
    But I would not say "morphisms". Things are closed under a certain operation, eg. division. "Integers are not closed under division, because dividing integers can give non-integers; but they are closed under addition, subtraction and multiplication". We don't say, "Integers are not closed under divisions, etc."
    But, your field might have a different convention (in the use of "with respect to"), and it's impossible to identify your field from your example. In any case, they appear to mean the same thing.
    Last edited by Raymott; 15-Mar-2014 at 06:28.

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