# 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

• Results about Alexandroff extensions can be found here.

## Source of Name

This entry was named for Pavel Sergeyevich Alexandrov.