Definition:Topology on Extended Real Numbers

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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.