
Dproperties of Finite unions of spaces with point countable weak bases and satisfying open(G)
 GUO Hongfeng, LI Yusi, SUN Weihua

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(10):
7276.
doi:10.6040/j.issn.16719352.0.2016.571

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The relation between pointcountable weak bases and Dproperty is studied. It is shown that, if a space X of countable tightness is the union of finitely many subspaces X_{i} with pointcountable weak base T_{i}={T_{i}(x):x∈X_{i}} satisfying T_{i}(x)∩T_{i}(y)=Ø for any distinct x,y∈X, then X is a Dspace. And then the relation is studied between open(G)and Dproperty. We obtain that, if X=X_{}1∪X_{}2, where both X_{1} and X_{2} satisfy open(G), then X_{}1^∩X_{}2^ 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 Dspace.