Abstract:  This paper is devoted to the images and preimages of D_o spaces.First of all,we prove that the  preimage X_o f a D_o space Y under a perfect mapping f is a D_o space whenever X has a G_i-diagonal or every  compact subset of X if G. And then we give a representation theorem of D_o spaces. At last,we give a characterization of countably compact D_o spaces.

Key words:  , D_o , space, paracompact M space, compact-covering mapping, open mapping, closed mapping, property wD