Name for the class of functions of the form $f:A^N\to A$

Question

Let $A$ be some space and $N$ be an integer. Does a function of the form $f:A^N\to A$ have a particular name? I'm looking for a keyword to see if there are any general properties of functions of this type.

Answer 1

$f$ is an operation on the set $A$ of arity $N.$ More specifically, a finitary operation.

Of course "operation" has many meanings, but this meaning is certainly common particularly when discussing algebraic theories in general. For example it is used in Grätzer's Universal Algebra, a standard reference.