Sequential closure

$[S]_{\text{Sequential}}$ = {$x \in X$ | x - sequential-point-of-closure}.

Connection with topological-closure

• $[S]{\text{Sequential}} \subset [S]{\tau}$

  Consider functions $[0, 1] \rightarrow \mathbb{R}$ with point-to-point-convergence topology.

  

Proposition

$[S]{\text{Sequential}} \subset [[S]{\text{Sequential}}]_{\text{Sequential}}$

Proof is obvious 😉

Example of strict inclusion: TODO