Definition. Let $E$ be a topological space. Suppose that $E$ contains a sequence $\{x_n\}$ such that for every $x\in E$, there exists a subsequence $\{x_{n_k}\}$ of $\{x_n\}$ with $x=\lim x_{n_k}$. Then we say $E$ enjoys sequential separability.

For a given topological space $X$, let $C_p(X)$ be the space of continuous functions on $X$ endowed with the point-wise topology. It is proved that $C_p(X)$ is separable iff $X$ is separably submetrizable (see this paper).

Question.

$$C_p(X) ~\textrm{is sequentially separable} \Leftrightarrow X=? $$