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

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous): Part $\text {II}$: Counterexamples: $49$. Right Order Topology