JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (10): 72-76.doi: 10.6040/j.issn.1671-9352.0.2016.571

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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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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

CLC Number: 

  • O189.1
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