摘要
先定义了柔集的笛卡尔积,射影序同态,柔拓扑空间的基、子基等概念,在此基础上定义了乘积柔拓扑空间,给出了乘积柔拓扑空间的等价描述以及乘积柔拓扑空间的一些基本性质,证明了一族满足T0分离性(resp.,T1分离性,T2分离性,正则分离性,连通性)的柔拓扑空间的乘积柔拓扑空间仍然满足这种性质,同时证明了第二可数是N0-可乘性质。
Firstly, the concepts of Cartesian product of the soft set, projective order-homomorphism, basis and subbasis of a soft topological space, are introduced. Based on these concepts, product soft topological space is defined, and characterizations of product soft topological spaces and basic properties of product soft topological spaces are given. It is proved that product soft topological space of a family of soft topological spaces with T0-separation （resp. , Tl-separation, Tz-separation, regular separation, connectedness） still has this kind property, and second-countability is 0-multiplicative property.
出处
《模糊系统与数学》
CSCD
北大核心
2013年第1期71-77,共7页
Fuzzy Systems and Mathematics
基金
国家自然科学基金资助项目(11071151)
陕西省自然科学基金资助项目(2010JM1005)
陕西师范大学研究生培养创新基金资助项目(2012CXS038)
关键词
柔集
柔拓扑空间
射影序同态
乘积柔拓扑空间
第二可数柔拓扑空间
连通柔拓扑空间
分离性
Soft Set
Soft Topological Space
Projective Order-homomorphism
Product Soft TopologicalSpace
Second-countable Soft Topological Space
Connected Soft Topological Space
Separation
