Prove Subset of Metric Space is Closed: Cluster Points

[ahct]

How can I prove that a subset of a metric space is closed if and only if it contains all its cluster points?

 

[Office_Shredder]

Start with the definition of a subset being closed, and figure out why that implies it contains all its cluster points. Then start with the definition of containing all its cluster points, and figure out why that implies the subset is closed.

If you post what you've tried so far we can help you further