Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $f$ is a $n$-ary function (where $n$ is any index set) and let every argument of $f$ may be zero or non-zero (for example, we can consider arguments of $n$ being posets with least element which I call "zero").

Are there any special name for such $f$ that every argument can be restored knowing the value of the function, provided that every of the $n$ arguments is non-zero?

An example of such $f$ is cartesian product of $n$ sets (where zero is the empty set).

share|cite|improve this question

The general terminology is that $f$ is invertible. For your specific example where $f$ is only invertible when all arguments are non-zero, then, assuming each argument of $f$ is in $\mathbb{C}$, this can be described by saying that $f|_{\mathbb{C}^{*n}}$ (the restriction of $f$ to $\mathbb{C}^{*n}$) is invertible ($\mathbb{C}^*$ being all nonzero elements of $\mathbb{C}$).

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.