Order, lattices, ordered algebraic structures Well-orders, well-founded orders, well-quasi-orders Concept
Directed set
Summary
A directed set is a nonempty preordered set in which every two elements have a common upper bound. Directed sets are the index sets of nets, which generalize sequences in topology, and of direct limits in algebra. They also underlie directed-complete partial orders in domain theory.
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12 pages build on this one.
Further reading
About this page
| Tag | D9RY4667K6 |
|---|---|
| URI | m2://D9RY4667K6 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 06A06, 54A20 |
| Specializes | Preorder |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Compact element
- Scott topology
- Way-below relation
- Domain theory
- Scott domain
- Directed-complete partial order
- Direct limit of algebras
- Direct limit
- Scott continuity
- Completeness in order theory
- Inverse limit
- Ideal completion