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## Homework Statement

the problem:

Let M be a metric in which the closure of every open set is open. Prove that M is discrete

## The Attempt at a Solution

To show M is discrete, it's enough to show every singleton set in M is open.

For any x in M, assume it's not open,

then there exist a converging sequence in M-{x} converges to x

I want to show such sequence does not exist, but I really don't know how to use the original statement that the closure of open set is open

Thank for help