拓扑空间的计算环境(英文)  

On computational environments of topological spaces

作　　者：黄方平[1] 梁基华[1] 

机构地区：[1]四川大学数学学院

出　　处：《四川大学学报（自然科学版）》2007年第4期765-773,共9页Journal of Sichuan University(Natural Science Edition)

基　　金：重庆市教委科学技术基金(KJ061102)

摘　　要：讨论了Tychonoff空间的计算环境.主要结论有:Choquet完备的弱domain,其极大点空间也是Choquet完备的;拓扑空间X是Tychonoff空间当且仅当X有一有界完备的弱环境;Tychonoff空间的Hausdorff紧化可以通过其计算环境实现.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.

关 键 词：弱domain环境 Choquet完备 Tychonoff空间 Hausdorff紧化 

分 类 号：O189.1[理学—数学]