Definition:Linearly Ordered Space

Definition
Let $\left({S, \preceq}\right)$ be a linearly ordered set.

Let $\tau$ be the order topology on $S$.

Then $\left({S, \preceq, \tau}\right)$ is a linearly ordered space.

Also known as
A linearly ordered space is also known as:
 * a totally ordered space
 * a linearly ordered topological space.

The last is often abbreviated as LOTS.