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- Containment_order abstract "In the mathematical field of order theory, a containment order is the partial order that arises as the subset-containment relation on some collection of objects. In a simple way, every poset P = (≤, X) is (isomorphic to) a containment order (like every group is isomorphic to a permutation group - Cayley's theorem). To see this, associate to each element x of X the setthen the transitivity of ≤ ensures that for all a and b in X, we haveThere can be sets of cardinal less than such that P is isomorphic to the containment order on S. The size of the smallest possible S is called the 2-dimension of S.Several important classes of poset arise as containment orders for some natural collections, like the Boolean lattice Qn, which is the collection of all 2n subsets of an n-element set, the dimension-n orders, which are the containment orders on collections of n-boxes anchored at the origin, and the interval-containment orders, which are precisely the orders of dimension ≤ 2. Other containment orders that are interesting in their own right include the circle orders, which arise from disks in the plane, and the angle orders.".
- Containment_order wikiPageID "11728075".
- Containment_order wikiPageRevisionID "594241508".
- Containment_order hasPhotoCollection Containment_order.
- Containment_order subject Category:Order_theory.
- Containment_order comment "In the mathematical field of order theory, a containment order is the partial order that arises as the subset-containment relation on some collection of objects. In a simple way, every poset P = (≤, X) is (isomorphic to) a containment order (like every group is isomorphic to a permutation group - Cayley's theorem).".
- Containment_order label "Containment order".
- Containment_order sameAs m.02rq8f4.
- Containment_order sameAs Q5164909.
- Containment_order sameAs Q5164909.
- Containment_order wasDerivedFrom Containment_order?oldid=594241508.
- Containment_order isPrimaryTopicOf Containment_order.