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**Homework Statement**

Show that every compact set must be closed.

I am looking for a simple proof.

This is supposed to be Intro Analysis proof.

**Relevant equations**

Any compact set must be bounded.

## The Attempt at a Solution

Suppose

*A*is not closed, so let

*a*be an accumulation point of

*A*such that

*a*is in

*A*etc. (I think I can finish this proof, but I do not like it.)

Does anyone know of a simpler proof.