摘要
本文证明了,若L是一个双完备的连续DCPO,则对所有的RW-空间X,函数空间[X→L]上的Isbell拓扑和Scott拓扑相同当且仅当L是有最小元的L-Domain.而且还证明了,若X是核紧的局部连通空间,则对所有有最小元的连续L-DomainL,[X→L]上的Isbell拓扑和Scott拓扑相同当且仅当X是RW-空间.特别地,若X是连续DCPO,则对所有有最小元的连续L-DomainL,函数空间[X→L]上的Isbell拓扑和Scott拓扑相同当且仅当X是RW-空间.这也给出由Lawson和Mislove提出的一个公开问题的一个部分回答.
It is proved in this paper that if L is a bicomplete continuous DCPO, then the Isbell and Scott topologies agree on function spaces [X → L] for all RW-spaces X iff L is an L-Domain with a least element. Moreover, it is obtained that, if X is a core compact and locally connected space, then the Isbell and Scott topologies agree on functions space [X → L] for all continuous L-Domain L with a least element if and only if X is an RW-space. Particularly, if X is a continuous DCPO, then the Isbell and Scott topologies agree on function spaces [X →L] for all continuous L-Domain L with a least element iff X is an RW-space. This also gives a partial solution to the open problem presented by Lawson and Mislove.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2005年第5期1021-1028,共8页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金资助项目教育部博士点基金资助项目
