More stratifiable function spaces

If X is a compact-covering image of a closed subspace of product of a σ-compact Polish space and a compact space, then C k ( X , M ) , the space of continuous maps of X into M with the compact-open topology, is stratifiable for any metric space M. s σ-compact Polish, K is compact and M metric then every point of C k ( X × K , M ) has a closure-preserving local base, and hence this function space is M 1 .