On Baire Category Properties of Function Spaces $C_k'(X,Y)$ - Banakh, Taras; Wang, Leijie (Topology Proceedings, 2020)
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 Gary Gruenhage and Daniel K. Ma. As a byproduct of the proof, we establish many interesting Baire category properties of the function spaces $C_k'(X,Y) = \left\{ f \in C_k(X,Y): f(X') \subseteq \{*_Y\} \right\}$, 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 $*_Y$.