4
$\begingroup$

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

Improve this question
$\endgroup$

1 Answer 1

Reset to default
3
$\begingroup$

N. V. Velichko, “On sequential separability,” Mat. Zametki 78 (5), 652–657 (2005) [Math. Notes 78 (5), 610–614 (2005)].

Improve this answer
$\endgroup$
1
  • $\begingroup$ A. V. Osipov, “The Separability and Sequential Separability of the Space C(X)”, Math. Notes, 104:1 (2018), 86–95 $\endgroup$ Commented Mar 27, 2022 at 8:08

You must log in to answer this question.

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.