Left and Right Order Topologies
Several variants of the order topology can be given:
- The right order topology on X is the topology whose open sets consist of intervals of the form (a, ∞).
- The left order topology on X is the topology whose open sets consist of intervals of the form (−∞, b).
The left and right order topologies can be used to give counterexamples in general topology. For example, the left or right order topology on a bounded set provides an example of a compact space that is not Hausdorff.
The left order topology is the standard topology used for many set-theoretic purposes on a Boolean algebra.
Read more about this topic: Order Topology
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