Definition:Complete Order Topology
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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.