Definition:Topology on Extended Real Numbers

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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 $\struct {\overline \R, \tau}$ may be referred to as the extended real number Space.

Also see

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