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 $\overline{\R}$.

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

Also see

 * Extended Real Number Space is Compact
 * Euclidean Space Subspace of Extended Real Number Space