## Proof That the Cartesian Product of Closed Sets is Closed

Theorem

Ifforeachthen

Proof

Let

Letwhereisopen inthenwhereisthe part ofwhereeachisexceptfor theth,which isWethen have

Henceand

Theorem

Ifforeachthen

Proof

Let

Letwhereisopen inthenwhereisthe part ofwhereeachisexceptfor theth,which isWethen have

Henceand