Definition:Sorgenfrey Line

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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

  • Results about the Sorgenfrey line can be found here.

Source of Name

This entry was named for Robert Henry Sorgenfrey.