On Jul 13, 12:29 pm, Rob Beezer <[email protected]> wrote:
> (a) a simple renaming, as perhaps "pre_image()"
>
> OR
>
> (b) make the existing  inverse_image()  method more capable:
> submodule in, submodule out  plus  element in, element out.
>
> At the risk of poisoning the well, I like (b), though in my textbook I
> call this (a).

Inverse image for a subset of the domain is usually defined to be the
complete inverse image, i.e., all elements of the domain that map to
it.
By identifying elements with singleton subsets, this would lead to
inverse_image meaning the appropriate coset of the kernel (or the
empty subset of the domain). I don't think there is a reasonable
alternative definition of preimage, so that might be the less
ambiguous term.

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