Definition:Order Topology/Definition 1

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

Let $\XX$ be the set of open rays in $S$.

Let $\tau$ be the topology on $S$ generated by $\XX$.

Then $\tau$ is called the order topology on $S$.

Also known as

The order topology is also known as the interval topology.

Also see