关于X_0-sn-网的一些性质

Some Properties on X_0-sn-networks

拓扑空间中的X_0-sn-弱第一可数空间与X_0-sn-网之间关系密切,拓扑空间X是X_0-sn-弱第一可数空间,且P是X中的一个点可数cs-网,如果P是有限交封闭的,则存在P的一个子族B,使得B是X的一个X_0-sn-网.证明得到以下条件等价:1)X具有点可数X_0-sn-网.2)存在一个度量空间M和一个序列商点可数映射f:M→X.3)存在一个度量空间M和一个序列商s-映射f:M→X,使得对x∈X,都有f-1(x)≤ω.

Let a topological space X be an X0-sn-weakly first-countable space,and P be a point-countable cs-network for X. The following results were obtained. If P was closed under finite intersections,then there existsed a subfamily B of P such that B was an X0-sn-network for X. It was also proved that the followings were equivalent for a topological space X： 1） X had a point-countable X0-sn-network. 2） There was a metric space M and a sequentially quotient,countable-to-one map f： M → X. 3） There was a metric space M and a sequentially quotient,s-map f： M → X such that f-1（ x） ≤ ω for each x ∈ X.