Definition:Order Topology/Definition 1

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Definition

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


Sources