Definition:Alexandroff Extension of Real Number Line

Definition
The Alexandroff extension of the real number line $\R^*$ is defined as:


 * $\R^* := \R \cup \set \infty$

that is, the set of real numbers together with an element $\infty$ which is not in $\R$.

Also see

 * Definition:Alexandroff Extension for a definition of this concept with respect to the general topological space.