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山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (10): 72-76.doi: 10.6040/j.issn.1671-9352.0.2016.571

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具有点可数弱基及满足开(G)条件的空间有限并的D-性质

郭洪峰1,2,李瑜斯1,孙伟华3   

  1. 1.山东财经大学数学与数量经济学院, 山东 济南 250014;2.山东大学控制科学与工程学院, 山东 济南 250061;3.山东大学(威海)数学与统计学院, 山东 威海 264209
  • 收稿日期:2016-12-05 出版日期:2017-10-20 发布日期:2017-10-12
  • 作者简介:郭洪峰(1979— ),男,博士,教授,研究方向为一般拓扑学与控制论. E-mail:guohongfeng@sdufe.edu.cn
  • 基金资助:
    山东省金融产业优化与区域发展管理协同创新中心项目(14XTYB017);国家自然科学基金资助项目(11501328);山东省自然科学基金资助项目(ZR2014JL003)支持;山东财经大学青年骨干教师境外研修重点支持计划资助

D-properties of Finite unions of spaces with point countable weak bases and satisfying open(G)

GUO Hong-feng1,2, LI Yu-si1, SUN Wei-hua3   

  1. 1. School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, Shandong, China;
    2. School of Control Science and Engineering, Shandong University, Jinan 250061, Shandong, China;
    3. School of Mathematics and Statistics, Shandong University(Weihai), Weihai 264209, Shandong, China
  • Received:2016-12-05 Online:2017-10-20 Published:2017-10-12

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摘要： 针对点可数弱基和开(G)条件与D-性质的联系分别进行了研究。 首先证明了:如果空间X具有可数紧度且X=∪{Xi:1≤i≤m},其中每个Xi具有点可数弱基Ti={Ti(x):x∈Xi}且对任意不同的x,y∈X,有Ti(x)∩Ti(y)=Ø,那么空间 X为D-空间。 然后证明了:如果X=X1∪X2,其中X1和X2都满足开(G)条件,那么X1^-∩X2^-满足开(G)条件。 在此基础上,对有限多个满足开(G)条件的空间的并是D-空间这一结论给出了详细的证明。

关键词: 开(G)条件, D-空间, 可数紧度, 弱基

Abstract: The relation between point-countable weak bases and D-property is studied. It is shown that, if a space X of countable tightness is the union of finitely many subspaces Xi with point-countable weak base Ti={Ti(x):x∈Xi} satisfying Ti(x)∩Ti(y)=Ø for any distinct x,y∈X, then X is a D-space. And then the relation is studied between open(G)and D-property. We obtain that, if X=X1∪X2, where both X1 and X2 satisfy open(G), then X1^-∩X2^- satisfies open(G). With the help of this result, a detailed proof is shown at last for the result that the union of finitely many subspaces satisfying open(G)is a D-space.

Key words: weak base, countable tightness, open(G), D-space

中图分类号: 

  • O189.1
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