关于弱拟第一可数空间的注记  

Remarks on weak-bases

作　　者：刘来山[1] 

机构地区：[1]泰州师范高等专科学校数学系,江苏泰州225300

出　　处：《高校应用数学学报（A辑）》2012年第3期375-378,共4页Applied Mathematics A Journal of Chinese Universities(Ser.A)

摘　　要：给出一个弱拟第一可数空间成为弱第一可数空间的充要条件,证明了空间是弱第一可数空间当且仅当它是具有序列点G_δ性质的弱拟第一可数空间且不含S_ω的闭拷贝,同时还证明了每一弱第一可数空间(弱拟第一可数空间)都是某个第一可数空间的商二到一映像(商可数到一映像),作为应用,部分回答了林寿(2007)的一个问题。The paper gives a sufficient and necessary condition for a weakly-weakly first-countable space to be a weakly first-countable space. It is proved that for a weakly-quasi first-countable space X, X is weakly first-countable if and only if X has the sequential point-Gδ property and no closed copies of Sw. We also prove that every weakly first-countable space （weakly-quasi first-countable space） is a quotient, two-to-one （countable-to-one） image of some first-countable space. As an application, a partial answer to a question posed by Lin Shou （2007） is obtained.

关 键 词：弱第一可数空间 弱拟第一可数空间 g可度量空间 

分 类 号：O189.11[理学—数学]