Category:Definitions/Sorgenfrey Line

This category contains definitions related to Sorgenfrey Line.
Related results can be found in Category:Sorgenfrey Line.

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.