Definition:Left Order Topology

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

Let $\tau$ be the topology on $S$ generated by the basis sets of the form:
 * $S_a = \set {x: x \prec a}$

for $a \in S$.

Then the topological space $\struct {S, \preccurlyeq, \tau}$ is known as the left order topology on $S$.

Also see

 * Definition:Order Topology
 * Definition:Right Order Topology