Interval Poset And Function Space On Domain

In this paper, we discuss the interval constructor on lattices and Bi-domains, andstudy the function spaces between two algebraic L-domains.Firstly, we obtain interval partial ordered sets(po-sets) on lattices by the intervalconstructor and the information order which be defined. If the lattice is complete,weakly atomic, and satisfies distributive law((JID)&(MID)), then the interval po-setis also the lattice respectively and satisfies these equivalent conditions. We also discussthe relation among R-filters, prime filters, congruences and quotients in lattice e?ectalgebra.Secondly, we construct new partial order relation on L-domain and FS-domain,obtain two new domains, that is Bi-L-domain and Bi-FS-domain. We introduce intervalconstructor and the information order into these Bi-domain categories, and prove thesecategories are closed under the interval constructor.At last, using the step functions, we investigate the function spaces between twoalgebraic L-domains, and obtain that the two function spaces are also algebraic L-domain.