In mathematics, an order topology is a certain topology that can be defined on any totally ordered set. It is a natural generalization of the topology of the real numbers to arbitrary totally ordered sets.
If X is a totally ordered set, the order topology on X is generated by the subbase of "open rays"
for all a,b in X. This is equivalent to saying that the open intervals
together with the above rays form a base for the order topology. The open sets in X are the sets that are a union of (possibly infinitely many) such open intervals and rays.
The order topology makes X into a completely normal Hausdorff space.
The standard topologies on R, Q, and N are the order topologies.
Read more about Order Topology: Induced Order Topology, An Example of A Subspace of A Linearly Ordered Space Whose Topology Is Not An Order Topology, Left and Right Order Topologies, Ordinal Space
Famous quotes containing the word order:
“To me the female principle is, or at least historically has been, basically anarchic. It values order without constraint, rule by custom not by force. It has been the male who enforces order, who constructs power structures, who makes, enforces, and breaks laws.”
—Ursula K. Le Guin (b. 1929)