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.

Also see

• Results about linearly ordered spaces can be found here.