Definition:Sorgenfrey Line
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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
- Results about the Sorgenfrey line can be found here.
Source of Name
This entry was named for Robert Henry Sorgenfrey.
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (next): Part $\text {II}$: Counterexamples: $51$. Right Half-Open Interval Topology