# Definition:Topology on Extended Real Numbers

(Redirected from Definition:Extended Real Number Space)

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## 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**.

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## Also see

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