Order, lattices, ordered algebraic structures Maps between ordered sets Concept
Closure operator
Summary
A closure operator on a partially ordered set is a map that is extensive, monotone and idempotent. It sends each element to the least "closed" element above it. Examples on power sets are topological closure, the linear span of vectors and the subgroup generated by a set. Closure operators on a power set correspond to Moore families.
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| Tag | 2HJGRABSPZ |
|---|---|
| URI | m2://2HJGRABSPZ |
| Kind | concept |
| Writing | W0 stub |
| MSC | 06A15 |
| Same as | |
| Changed | 2 November 2026 |
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