Sequential point of closure

Let $(X, \tau)$ - a topological-space.

A point $x \in X$ is a sequential point of closure of $S \subset X$ if $$ \exists {x_n} \subset S: x_n \rightarrow x $$

Here convergence is a topology-convergence

Connection with point-of-closure

• $x$ is a sequential point of closure $\implies$ $x$ is a point-of-closure

Example

when sequential points of closure are the subset of points of closure: