On computational environments of topological spaces

As has been disclosed by Martin,a large number of important topological spaces do not have any continuous domain as their computational models.So it is of interest to study new kinds of pragmatic computational environments so as to model more topological spaces.The authors focus on those bounded complete continuous posets with enough maximal points,and show that they are good choice for computational environments of those Tychonoff spaces with no directed complete model.It is proved that the maximal point spaces of a Choquet complete weak domain is also Choquet complete.And it is proved that X is a Tychonoff space iff X has a bounded complete weak domain environment.And it is also shown that Hausdorff compactifications of Tychonoff spaces can be realized via some of its computational environments.