enow.com Web Search

Search results

1. Results from the WOW.Com Content Network

2. Partially ordered set - Wikipedia

   en.wikipedia.org/wiki/Partially_ordered_set

   A partially ordered set (poset for short) is an ordered pair = (,) consisting of a set (called the ground set of ) and a partial order on . When the meaning is clear from context and there is no ambiguity about the partial order, the set X {\displaystyle X} itself is sometimes called a poset.

3. Order theory - Wikipedia

   en.wikipedia.org/wiki/Order_theory

   A set with a partial order on it is called a partially ordered set, poset, or just ordered set if the intended meaning is clear. By checking these properties, one immediately sees that the well-known orders on natural numbers , integers , rational numbers and reals are all orders in the above sense.

4. Join and meet - Wikipedia

   en.wikipedia.org/wiki/Join_and_meet

   Join and meet are dual to one another with respect to order inversion. A partially ordered set in which all pairs have a join is a join-semilattice. Dually, a partially ordered set in which all pairs have a meet is a meet-semilattice. A partially ordered set that is both a join-semilattice and a meet-semilattice is a lattice.

5. Lattice (order) - Wikipedia

   en.wikipedia.org/wiki/Lattice_(order)

   A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).

6. Partially ordered group - Wikipedia

   en.wikipedia.org/wiki/Partially_ordered_group

   A partially ordered group G is called integrally closed if for all elements a and b of G, if a n ≤ b for all natural n then a ≤ 1. [1]This property is somewhat stronger than the fact that a partially ordered group is Archimedean, though for a lattice-ordered group to be integrally closed and to be Archimedean is equivalent. [2]

7. Compact element - Wikipedia

   en.wikipedia.org/wiki/Compact_element

   The set Sub(A), ordered by set inclusion, is a lattice. The greatest element of Sub(A) is the set A itself. For any S, T in Sub(A), the greatest lower bound of S and T is the set theoretic intersection of S and T; the smallest upper bound is the subalgebra generated by the union of S and T. The set Sub(A) is even a complete lattice.

8. Dedekind–MacNeille completion - Wikipedia

   en.wikipedia.org/wiki/Dedekind–MacNeille...

   As Jourdan, Rampon & Jard (1994) observe, the problem of listing all cuts in a partially ordered set can be formulated as a special case of a simpler problem, of listing all maximal antichains in a different partially ordered set. If P is any partially ordered set, let Q be a partial order whose elements contain two copies of P: for each ...

9. Completeness (order theory) - Wikipedia

   en.wikipedia.org/wiki/Completeness_(order_theory)

   In the mathematical area of order theory, completeness properties assert the existence of certain infima or suprema of a given partially ordered set (poset). The most familiar example is the completeness of the real numbers. A special use of the term refers to complete partial orders or complete lattices. However, many other interesting notions ...