广西科学
廣西科學
엄서과학
GUANGXI SCIENCES
2007年
4期
354-356
,共3页
陈海燕%王培%刘士琴%郑顶伟
陳海燕%王培%劉士琴%鄭頂偉
진해연%왕배%류사금%정정위
()0-弱基%()-空间%sn-度量空间%sn-第一可数%cs*-网%cs-网
()0-弱基%()-空間%sn-度量空間%sn-第一可數%cs*-網%cs-網
()0-약기%()-공간%sn-도량공간%sn-제일가수%cs*-망%cs-망
()0-weak base%()-space%sn-metric space%sn-first countable%cs*-network%cs-network
证明在空间X中下列论述等价:(1)X有σ-离散的()0-弱基;(2)X有σ-局部有限的()0-弱基;(3)X是()0-弱第一可数的()空间,()0-弱基是开、闭遗传的,点可数()0-弱基是cs*-网.并讨论()0-弱基,sn-网,cs-网以及cs*-网的关系.
證明在空間X中下列論述等價:(1)X有σ-離散的()0-弱基;(2)X有σ-跼部有限的()0-弱基;(3)X是()0-弱第一可數的()空間,()0-弱基是開、閉遺傳的,點可數()0-弱基是cs*-網.併討論()0-弱基,sn-網,cs-網以及cs*-網的關繫.
증명재공간X중하렬논술등개:(1)X유σ-리산적()0-약기;(2)X유σ-국부유한적()0-약기;(3)X시()0-약제일가수적()공간,()0-약기시개、폐유전적,점가수()0-약기시cs*-망.병토론()0-약기,sn-망,cs-망이급cs*-망적관계.
It is proved that the followings are equivalent for a space X: (1) X has a σ-discrete ()0-weak base;(2)X has a σ-locally finite ()0-weak base;(3)X is a ()0-weakly first-countable and ()-space,space with ()0-weak base is open, closed hereditary,and point-countable ()0-weak base is cs*-network.Some relations are discussed among ()0-weak base,sn-network,cs-network and cs*-network.
