Definition:Generalized Ordered Space

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

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

Equivalence of Definitions
That the definitions above are equivalent is shown in Equivalence of Definitions of Generalized Ordered Space.

Also known as
A generalized ordered space is often called a GO-space.

Linguistic Note
The UK English spelling renders generalised ordered space.

Also see

 * Definition:Linearly Ordered Space