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directed set

A Dictionary of Computing | 2004 | 284 words | Copyright

directed set A subset X of a partially ordered set S, such that every finite subset of X has an upper bound in X itself. As a special case of this, a chain is a countable subset of the form x0 ⊆ x1 ⊆ x2 ⊆ …

where ⊆ denotes the partial ordering on S.

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