Definition:Generalized Ordered Space/Definition 2

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 iff:
 * There exists a linearly ordered space $\left({X',\preceq',\tau'}\right)$ and a mapping $\phi: X \to X'$ such that $\phi$ is an order embedding and a Topological Embedding