Uncountable Closed Ordinal Space is Lindelöf

Theorem
Let $\Omega$ denote the first uncountable ordinal.

Let $\closedint 0 \Omega$ denote the closed ordinal space on $\Omega$.

Then $\closedint 0 \Omega$ is a Lindelöf space.

Proof
We have:
 * Closed Ordinal Space is Compact
 * Compact Space is Lindelöf