A Set is Closed in a Metric Space iff it contains all its Sequential Limits
# Statement
Suppose $(M, d)$ is a Metric Space and $S \subset M$. Then $S$ is Closed If and Only If $S$ contains all of it’s sequential limits.
Search
Suppose $(M, d)$ is a Metric Space and $S \subset M$. Then $S$ is Closed If and Only If $S$ contains all of it’s sequential limits.