# Topology/Order

< Topology

Recall that a set is said to be totally ordered if there exists a relation satifying for all

- (antisymmetry)
- (transitivity)
- (totality)

The usual topology on is defined so that the open intervals for form a base for . It turns out that this construction can be generalized to any totally ordered set .

## Definition[edit]

Let be a totally ordered set. The topology on generated by sets of the form or is called the **order topology** on