The Space Of The Maximal Points In The Mixed Power Domain And The Closedown Of Its Construction With Respect To Some Kind Of Domain

Power domains introduced for modeling nondeterministic computation have become the most important constructions in the semantics of nondeterministic programming languages.Several classic power domains have been studied deeply(in [5]).C.A.Gunter introduced the concept of the mixed power domain in [6].And he gave a description of the mixed power domain by order for a sober ground domain D.So we can understand it more clearly.However,the mixed power domain isn't studied deeply till now. As an important construction,it is necessary to be discussed seriously.At frst,such a mixed power domain constructed by the ground domain D which is continous and Lawson compact will be discussed.At first,we've given some basic properties of the mixed power domains constructed by ordinary domains. And in recent years,it has attracted much attention in applying the hull of domains to resolve some problems in topology(see [8,9,10]). So we discussed the hull of the mixed power domain for deeper consideration. In this paper a characterization of the maximal elements in the mixed power domain has been given,and we have also proved the mixed power domain is the hull of its maximal space for a Lawson compact domain D.And secendly,we discussed the closedown of FB-domain with respect tothe construction of the mixed power domains. A basic requirment for a domain category becoming the model of an non- deterministic programming language is that it should be closed with a kind of power domain construction. So it has turned into a basic task to study the domain categories which are closed with some kind of power domain constructions(see [2]).And in this paper,we proved that FB-domain is closed with respect to the mixed power domain construction.