Definition:Generalized Ordered Space/Definition 1

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

Let $\tau$ be a topology for $X$.

Then $\left({X, \preceq, \tau}\right)$ is a generalized ordered space :


 * $(1): \quad \left({X, \tau}\right)$ is a Hausdorff space


 * $(2): \quad$ There exists a basis for $\left({X, \tau}\right)$ whose elements are convex in $X$.

Also see

 * Equivalence of Definitions of Generalized Ordered Space