Countable Discrete Space is Lindelöf

Theorem
Let $T = \struct {S, \tau}$ be a countable discrete topological space.

Then $T$ is a Lindelöf space.

Proof
We have:
 * Countable Discrete Space is $\sigma$-Compact
 * $\sigma$-Compact Space is Lindelöf

So if $S$ is countable, $T$ is a Lindelöf space.

Also see

 * Uncountable Discrete Space is not Lindelöf