Deleted Integer Topology is Lindelöf

Corollary to Deleted Integer Topology is Second-Countable
Let $S = \R_{\ge 0} \setminus \Z$.

Let $\tau$ be the deleted integer topology on $S$.

The topological space $T = \left({S, \tau}\right)$ is Lindelöf.

Proof
From Deleted Integer Topology is Second-Countable, $T$ is second-countable.

The result follows from Second-Countable Space is Lindelöf.