超连续domain上的投射

The projection on hypercontinuous domains

本文给出了一个反例说明超连续domain L在Scott连续闭包算子c下的像c(L)不一定是超连续domain,证明了若超连续domain L上的Scott连续投射p有上伴随或有下伴随,则p(L)是超连续domain;若超代数domain L上的Scott连续闭包算子c有上伴随或有下伴随,则c(L)是超代数domain.

In this paper, we give a counterexample to show that for an upper-continuous closure operator c on the hyperalgebraic domain L, c（L） is not a hypercontinuous domain. It is proved that if p is a Scott-continuous projection on a hypercontinuous domain L and p is a lower （upper） adjoint, then p（L） is a hypercontinuous domain. We also show that if c is a Scott-continuous closure operator on the hyperalgebraic domain L and c is a lower （upper） adjoint, then c（L） is a hyperalgebraic domain.