κ-Fréchet Urysohn property of Ck(X)

For a Tychonoff space X, we denote by Ck(X) the space of all real-valued continuous functions on X with the compact open topology. A space X is said to be κ-Fréchet Urysohn if for every open subset U of X and every , there exists a sequence {xn}n∈ω⊂U converging to x. In this paper, we show that Ck(X) is κ-Fréchet Urysohn iff every moving off family of compact subsets of X has a countable subfamily which is strongly compact-finite. In particular, we obtain that every stratifiable Baire space Ck(X) is an M1-space.