The Study Of The Countable AD-spaces

This article defines the concept of countable-aD-space,through the study of some properties of the countable-aD-space,we prove that the closed subspaces of countable-aD-space are countable-aD-space;if X=Y∪Z and X is a T1-space,Y and Z are both countable-aD-subspace,then X is a countable-aD-space;if X is the union of countable closed countable-aD-subspace,then X is a countable-aD-space;the inverse spaces of countable-aD-space into perfect mapping is a countable-aD-space;the image spaces of countable-aD-space under continuous closed mapping is a countable-aD-space;the other covering properties of countable-aD-space:if the Lindelof and T1 space X is the union of a metalindelof subspaces and a countable-aD-subspace,then X is a countable-aD-space;if the Lindelof and T1 space X is the union of finite metalindelof subspaces,then X is a countable-aD-space;if X is a Lindelof and T1 space,and it is the union of finiteδθ-refinable subspaces,then X is a countable-aD-space.