Definition:Countable Complement Extension Topology

Theorem
Let $\R$ denote the real number line.

Let $\tau_d$ be the Euclidean topology on $\R$.

Let $\tau_c$ be the countable complement topology $\R$.

Let $\tau$ be the smallest topology generated by $\tau_c \cup \tau_d$.

$\tau$ is known as the countable complement extension topology on $\R$.