For certain property ℜ of topological T0-spaces, we prove that if T0-space Y has property ℜ, then [X,Y] endowed with the Isbell topology possesses ℜ for any T0-space X ; and if X has property ℜ for some non-empty space X, then so does Y.

The class of well-filtered spaces is one of the important class of topological spaces in domain theory. Recently, the existence of well-filterification of T0-spaces has been established. In this paper, we introduce the definition of wf-rank and prove that for any ordinal α, there exists a T0-space whose wf-rank equals α.