# 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.

## Also see

• Results about the extended real number space can be found here.