拟连续Domain的遗传性、不变性及映射空间  

The heredity,invariance and mapping space of quasicontinuous Domains

作　　者：赵娜娜[1] 赵彬[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《陕西师范大学学报（自然科学版）》2010年第6期18-22,共5页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10871121)

摘　　要：讨论了拟连续Domain的遗传性、不变性及映射空间.证明了拟连续Domain及拟代数Domain对开子空间和闭子空间都是可遗传的,拟连续Domain及拟代数Domain在保持集与集之间的way below-preserving序的拟Scott连续映射下保持不变.对于有界完备拟连续DomainX和L,当L是全序时,由Scott连续映射构成的映射空间[X→L]是有界完备拟连续Domain.The heredity,invariance and mapping space of quasicontinuous Domains are discussed.It is proved that quasicontinuous Domains and quasialgebraic Domains are hereditary for scott open subsets and scott closed subsets,and the images of a quasicintinuous domain and a quasialgebraic Domain under the way below-preserving quasi-Scott continuous map are still quasicontinuous and quasialgebraic,respectively.It is shown that if X and L are bounded complete quasicontinuous Domains and L is totally ordered,then the mapping space of all Scott continuous maps is a bounded complete quasicontinuous Domain.

关 键 词：拟连续DOMAIN 拟代数Domain Domain子空间 步映射 映射空间 

分 类 号：O153.1[理学—数学]