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Topology/Order
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Topology Order Subspaces Order Topology
Recall that a set is said to be totally ordered if there exists a relation satisfying for all
(antisymmetry)
(transitivity)
(totality)
The usual topology on is defined so that the open intervals for form a base for . It turns out that this construction can be generalized to any totally ordered set .
Definition
Let be a totally ordered set. The topology on generated by sets of the form or is called the order topology on
Topology Order Subspaces Order Topology
Topology