Function spaces which are stratifiable

Let X be a compact metric space and Y a stratifiable space. By C(X,Y), we denote the space of continuous of continuous maps from X to Y with the compact-open topology. In general, C(X,Y) is not stratifiable. In this paper, we show that C(X,Y0 is stratifiable if Y satisfies the condition given by Mizokami [Mi]. And we construct a stratifiable space Y such that C(X,Y) in not stratifiable even if X is countable and compact