Partial Orders in Topological Spaces
If P is a partially ordered set that has also been given the structure of a topological space, then it is customary to assume that {(a, b) : a ≤ b} is a closed subset of the topological product space . Under this assumption partial order relations are well behaved at limits in the sense that if, and ai ≤ bi for all i, then a ≤ b.
Read more about this topic: Partially Ordered Set
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