@article{article_479607, title={On selective sequential separability of function spaces with the compact-open topology}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={48}, pages={1761–1766}, year={2019}, DOI={10.15672/HJMS.2018.635}, url={https://izlik.org/JA68BF55ET}, author={V. Osipov, Alexander}, keywords={compact-open topology,function space,selectively sequentially separable,S1(S,S),sequentially dense set,property 2,property 4}, abstract={For a Tychonoff space $X$, we denote by $C_k(X)$ the space of all real-valued continuous functions on $X$ with the compact-open topology. A subset $A\subset X$ is said to be sequentially dense in $X$ if every point of $X$ is the limit of a convergent sequence in $A$. A space $C_k(X)$ is selectively sequentially separable (in Scheepers’ terminology: $C_k(X)$ satisfies $S_{fin}(\mathcal{S},\mathcal{S})$) if whenever $(S_n : n\in \mathbb{N})$ is a sequence of sequentially dense subsets of $C_k(X)$, one can pick finite $F_n\subset S_n$ ($n\in \mathbb{N}$) such that $\bigcup \{F_n: n\in \mathbb{N}\}$ is sequentially dense in $C_k(X)$. In this paper, we give a characterization for $C_k(X)$ to satisfy $S_{fin}(\mathcal{S},\mathcal{S})$.}, number={6}