Definition:Linearly Ordered Space

Definition
Let $\struct {S, \preceq}$ be a linearly ordered set.

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

Then $\struct {S, \preceq, \tau}$ 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 can sometimes be seen abbreviated as LOTS.