# Contents

## Definition

Given a linearly ordered set $(S, \lt)$, its order topology is the topology on $S$ generated from the sub-basis $\beta \subset P(S)$

$\beta \coloneqq \left\{ (a,\infty), (-\infty,a) \right\}_{a \in S} \,.$

whose elements are the “open half rays”

$(a, \infty) \coloneqq \left\{ s \in S \,\vert\, a \lt s \right\} \phantom{AAAA} (-\infty, a) \coloneqq \left\{ s \in S \,\vert\, s \lt a \right\} \,.$

## References

Revised on May 3, 2017 17:44:21 by Toby Bartels (70.198.52.201)