Definition:Sorgenfrey Line

Definition
Let $\R$ be the set of real numbers

Let $\BB$ be the set:
 * $\BB = \set {\hointr a b: a, b \in \R}$

where $\hointr a b$ is the half-open interval $\set {x \in \R: a \le x < b}$.

Then $\BB$ is the basis for a topology $\tau$ on $\R$.

The topological space $T = \struct {\R, \tau}$ is referred to as the Sorgenfrey line.

Also known as
The Sorgenfrey line is also found in the literature referred to as:
 * the lower limit topology
 * the right half-open interval topology.

Also see

 * Sorgenfrey Line is Topology