具有点可数弱基及满足开(G)条件的空间有限并的D-性质

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=∪{X_i:1≤i≤m},其中每个X_i具有点可数弱基T_i={T_i(x):x∈X_i}且对任意不同的x,y∈X,有T_i(x)∩T_i(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。

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

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 X_i with point-countable 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 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.