Definition:Topology on Extended Real Numbers

This page has been identified as a candidate for refactoring of basic complexity. Until this has been finished, please leave {{Refactor}} in the code. New contributors: Refactoring is a task which is expected to be undertaken by experienced editors only. Because of the underlying complexity of the work needed, it is recommended that you do not embark on a refactoring task until you have become familiar with the structural nature of pages of $\mathsf{Pr} \infty \mathsf{fWiki}$. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Refactor}} from the code.

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

This article is complete as far as it goes, but it could do with expansion. In particular: Make this an example of Definition:Order Topology You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Expand}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Also see

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