Other operations can be defined for sets with elements of a special type:

The algebraic operations on are defined via these maps in the obvious manner.

The operation could not easily be defined as a Western crusade.

The values for which an operation is defined form a set called its domain.

Additionally, in the usual lattice operations (meet and join) are defined.

The operation of Out(F) on the outer space is defined as follows.

Administrative operations may be defined on both object categories.

All operations on complex numbers are defined in header.

These operations are defined naturally as if the variable was an element of .

The operations are also defined with just a label, and this label must be unique too, but only within the standard.