Dominated Ideals and Baire Ideals in Complete Domains

We consider an operator Gi,I generated by a given interior operator i and an ideal I. Among the properties of the operator Gi,I, two properties denoted by Pi and Qi are remarkable. The ideals with the property Pi are called dominated ideals, and the ideals with the property Qi are called Baire ideals. We present methods of constructing dominated and Baire ideals, providing several examples and (topological) results in the framework of domain theory.