Hereditability Of Hypercontinuous Domains And Quasi-hypercontinuous Domains

In this paper,It is proved that quasi-hypercontinuous domains are hereditary for upper open subsets,A counterexample is constructed to show that quasihypercontinuous domains are not hereditary for upper closed subsets.We prove that retractions of(quasi-hypercontinuous)hypercontinuous domains are(quasihypercontinuous)hypercontinuous domains.we give a counterexample to show that for an upper-continuous closure operator c on the hyperalgebraic domain L,c(L)is not a quasi-hypercontinuous domain.It is proved that if p is a Scottcontinuous projection on a(quasi-hypercontinuous)hypercontinuous domain L and p is a lower(upper)adjoint,then p(L)is a(quasi-hypercontinuous)hypercontinuous domain.We also show that if c is a Scott-continuous closure operator on the(quasi-hyperalgebraic)hyperalgebraic domain L and c is a lower(upper)adjoint,then c(L)is a(quasi-hyperalgebraic)hyperalgebraic domain.