# Definition:Sorgenfrey Line

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## 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

• Results about the Sorgenfrey line can be found here.

## Source of Name

This entry was named for Robert Henry Sorgenfrey.