Compact Complement Topology is Separable/Proof 2

Theorem

Let $T = \struct {\R, \tau}$ be the compact complement topology on $\R$.

Then $T$ is a separable space.

Proof

We have that:

Rationals are Dense in Compact Complement Topology

Rational Numbers are Countably Infinite

Hence the result by definition of separable space.

$\blacksquare$