Definition:Linearly Ordered Space

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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.