Dominated Ideals and Baire Ideals in Complete Domains

Dănuţ Rusu () and Gabriel Ciobanu
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Dănuţ Rusu: Faculty of Mathematics, Alexandru Ioan Cuza University, 700505 Iaşi, Romania
Gabriel Ciobanu: Romanian Academy, 700481 Iaşi, Romania

Mathematics, 2024, vol. 12, issue 21, 1-10

Abstract: We consider an operator G i , I generated by a given interior operator i and an ideal I . Among the properties of the operator G i , I , two properties denoted by P i and Q i are remarkable. The ideals with the property P i are called dominated ideals, and the ideals with the property Q i 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.

Keywords: domain theory; ideals in complete domains; interior operators generated by ideals (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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