The set of all partial functions (partial transformations) on a given base set, forms a regular semigroup called the semigroup of all partial transformations (or the partial transformation semigroup on ), typically denoted by The set of all partial bijections on forms the symmetric inverse semigroup.
The set of all partial functions (partial transformations) on a given base set, forms a regular sem,igroup called the semigroup of all partial transformations (or the partial transformation semigroup on ) typically denoted by The set of all partial bijections on forms the symmetric inverse semigroup.