# Proof of an equality

1. Oct 15, 2011

### gotjrgkr

Let A be a metric space and B be a compact subset of A.
Is it true that an equality B = Int(B) $\cup$ bd(B) holds??

2. Oct 15, 2011

### HallsofIvy

In a metric space every compact set is closed (actually in every topological space). What does that tell you about its boundary points?

3. Oct 15, 2011

### gotjrgkr

Boundary point is also limit point, right?
Then it belongs to B since B is closed?

4. Oct 15, 2011

### spamiam

Hausdorff topological space, no? Which does include metric spaces, I admit.