Definition:Complete Order Topology

Definition

Let $\struct {S, \preceq}$ be a complete ordered set.

Let $\tau$ be the order topology on $\struct {S, \preceq}$.

Then $\tau$ is a complete order topology.

Hence $\struct {S, \preceq, \tau}$ is a complete order space.

Also see

• Results about complete order topologies can be found here.