Definition:Order Topology/Definition 1
Jump to navigation
Jump to search
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
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $39$. Order Topology