Definition:Right Order Topology
Jump to navigation
Jump to search
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:
- $S_a = \set {x: a \prec x}$
for $a \in S$.
Then the topological space $\struct {S, \preccurlyeq, \tau}$ is known as the right order topology on $S$.
Also see
- Results about the right order topology can be found here.
Examples
- Definition:Right Order Topology on Strictly Positive Integers
- Definition:Right Order Topology on Real Numbers
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (next): Part $\text {II}$: Counterexamples: $49$. Right Order Topology