Order, lattices, ordered algebraic structures Binary relations and basic order notions Concept
Upper set
Summary
An upper set of a partially ordered set is a subset that contains everything above each of its elements. The dual notion is a lower set, which contains everything below each of its elements. Upper and lower sets are used to define order filters, the Alexandrov topology, and the lattice of down-sets of a poset.
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About this page
| Tag | ETCE287E2R |
|---|---|
| URI | m2://ETCE287E2R |
| Kind | concept |
| Writing | W0 stub |
| MSC | 06A06 |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Esakia space
- Scott topology
- Order polytope
- Alexandrov topology
- Priestley space
- Priestley duality
- Order filter