Definition:Sorgenfrey Line

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

Let $\mathcal B$ be the set:
 * $\mathcal B = \left\{{\left[{a \,.\,.\, b}\right): a, b \in \R}\right\}$

where $\left[{a \,.\,.\, b}\right)$ is the half-open interval $\left\{{x \in \R: a \le x < b}\right\}$.

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

The topological space $T = \left({\R, \tau}\right)$ 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