Returning to 2-adic relations, it is useful to describe several familiar classes of objects in terms of their local and numerical incidence properties. Let be an arbitrary 2-adic relation. The following properties of can be defined.
If is tubular at then is called a partial function or a prefunction from to This is sometimes indicated by giving an alternate name, for example, and writing Thus we have the following definition.
If is a prefunction which happens to be total at then is called a function from to indicated by writing To say a relation is totally tubular at is to say it is -regular at Thus, we may formalize the following definition.
In the case of a function we have the following additional definitions.