凸幂Domain的极大点的注记  

Note on the Maximal Points of the Convex-Power Domain

作　　者：奚小勇[1] 

机构地区：[1]四川大学数学学院,成都610064

出　　处：《数学学报（中文版）》2005年第4期821-828,共8页Acta Mathematica Sinica：Chinese Series

基　　金：教育部博士点基金资助项目

摘　　要：本文讨论了连续Domain D的极大点Max(D)的紧子集Com(Max(D))与凸幂Domain CD的极大点Max(CD)一一对应的条件以及Max(CD)上拓扑的性质, 证明了当X为局部紧Hausdorff空间时,X的上空间UX的凸幂Domain C(UX)的极大点Max(C(UX))与Com(Max(UX))(即X的紧子集)一一对应.X的上空间UX上的Lawson拓扑与X紧子集上的Vietoris拓扑相同,并且与Max(C(UX))带有C(UX)上的相对Scott拓扑同胚.We discuss in this paper that when the compact subset Com(Max (D)) of the maximal points Max(D) of continuous Domain D and the maximal points Max(CD) of convex-power Domain CD are one-to-one correspondence. Particularly, it is proved that for upper space UX of locally compact Hausdorff space X, Com(Max(UX))(i.e. the set of the compact subset of X)and maximal points Max(C(UX)) of the convex power Domain C(UX) are one to one. In this case Lawson topology on upper space UX agree with the Vietoris topology on Com(Max(UX)), which is homeomorphic to Max(C(UX)) with the Scott topology inherited from the C(UX).

关 键 词：极大点 凸幂Domain VIETORIS拓扑 

分 类 号：O189.1[理学—数学] O153.1[理学—基础数学]