Formal Cover Space And Weakly (?) - The Nature Of The Space Can Be Added

In this paper, a series of properties of normal screenable spaces and normal and weakly (?)- refinable spaces are given. It is proved emphasizely that:Theoreml Let paracompact, |∑|=λ, then it is normal screenable space iff is normal screenable space for everyTheorem2 For countable paracompace ,the followings are equivalent: (1) X is normal screenable space; (2) is normal screenable space; (3) is normal screenable space.Theorem3 Let every be open and ontomapping ,(1) if X isλ-paracompact and every X_σis normal and weakly (?)- refinable, then X is normal and weakly (?)- refinable;(2) if X is hereditarilyλ-paracompact and every X_σis hereditarily normal and hereditarily weakly (?)- refinable , then X is hereditarily normal and hereditarily weakly (?)- refinableTheorem4 (1) If X is metacompact and the countable union of closed base-metacompact sets relative to X,then ;X is base-metacompact; (2) Let X be base-metacompact .If M (?) X is an F_σset withω(M)=ω(X), then X is base-metacompact.