Ideals in Heyting semilattices and open homomorphisms

Abstract

In the general context of Heyting lattices, the ideals, an extension of the concept of the sublocale set of a locale, are studied. Among other the class of Heyting lattices (and in particular the class of locales) in which open homomorphisms coincide with the complete ones, is characterized.

Keywords

• Ideals
• Heyting
• semilattices
• homomorphisms