\begin{definition}[Definition:Generalized Ordered Space/Definition 2]
Let $\struct {S, \preceq}$ be a totally ordered set.
Let $\tau$ be a topology on $S$.
$\struct {S, \preceq, \tau}$ is a '''generalized ordered space''' {{iff}}:
:$(1): \quad$ there exists a linearly ordered space $\struct {S', \preceq', \tau'}$
:$(2): \quad$ there exists a mapping $\phi: S \to S'$ such that $\phi$ is both an order embedding and a topological embedding.
\end{definition}