Function spaces which are stratifiable

Abstract

Let $X$ be a compact metric space and $Y$ a stratifiable space. By $C(X, Y)$, we denote the space 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 $C(X, Y)$ is stratifiable if $Y$ satisfies the condition given by Mizokami [Mi]. And we construct a stratifiable space $Y$ such that $C(X, Y)$ is not stratifiable even if $X$ is countable and compact.