On Baire category properties of function spaces $C_k'(X,Y)$

Abstract

We prove that for a stratifiable scattered space $X$ of finite scattered height, the function space $C_k(X)$ endowed with the compact-open topology is Baire if and only if $X$ has the Moving Off Property of Gruenhage and Ma. As a byproduct of the proof we establish many interesting Baire category properties of the function spaces $C_k'(X,Y)=\{f\in C_k(X,Y):f(X')\subset\{*_Y\}\}$, where $X$ is a topological space, $X'$ is the set of non-isolated points of $X$, and $Y$ is a topological space with a distinguished point $*_Y$.