【摘要】 本文给出了空间为D-空间的一充分条件,主要结论如下:如果空间X有一点可数族F,满足对X的任一子集A■X,若A在X中不闭,都存在某点x∈■\A,使得对X的任一开集U,若x∈U,都存在某个F∈F,使得x∈F■U且F∩A≠■,则X是D-空间.由此结论,我们得到一序列空间若有点可数cs~*-网络,则X是D-空间.更多还原

【Abstract】 In this note,we give a sufficient condition that a space to be a D-space.The following is the main conclusion:If a space X has a point-countable family F,such that for any set A■X,if A is not closed in X,then there exists some point x∈■\A,satisfying that for any open set U of X,suppose x∈U,there exists some F∈F,such that x∈F■U and F∩A≠■.Then X is a D-space.By this result,we will know that a sequential space with a point-countable cs~*-network is a D-space.更多还原