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 ← Subspaces Order Order Topology → 

Recall that a set is said to be totally ordered if there exists a relation satifying for all

  1. (antisymmetry)
  2. (transitivity)
  3. (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 .


Let be a totally ordered set. The topology on generated by sets of the form or is called the order topology on

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