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) = { f C_k(X,Y): f(X’) {*_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.