Definition:Topology on Extended Real Numbers

Definition
Let $\overline{\R}$ denote the extended real numbers.

The (standard) topology on $\overline{\R}$ is the order topology $\tau$ associated to the ordering on $\overline{\R}$.

Extended Real Number Space
The topological space $\left({\overline{\R}, \tau}\right)$ may be referred to as the extended real number space.