Definition:Linearly Ordered Space

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

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

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

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

The last is often abbreviated as LOTS.