complete lattice


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complete lattice

[kəm′plēt ′lad·əs]
(mathematics)
A partially ordered set in which every subset has both a supremum and an infimum.

complete lattice

A lattice is a partial ordering of a set under a relation where all finite subsets have a least upper bound and a greatest lower bound. A complete lattice also has these for infinite subsets. Every finite lattice is complete. Some authors drop the requirement for greatest lower bounds.
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Let L be a complete lattice. [Lambda]X, Y.X [right arrow] Y: p(L) [right arrow] p(L) is argumentwise additive in <p(L), [subset or is equal to]).
A continuous poset which is also a complete lattice is called a continuous lattice.
It is a complete lattice, that is, a set P and a binary partial order relation.
where A is the underlying set, [L.sub.A] is a complete lattice with the least element [0.sub.A] and the greatest element [1.sub.A], and
on the complete lattice uco(C) of all (upper) closure operators on C.
Fora bc-dcpo L, let M [subset or equal to] L and [L.sup.T] = Lu{T} be the complete lattice obtained from L by adjoining a top element T.
Note first that [t.sup.*] = [disjunction]] indeed exists since ([0,1], [disjunction], [conjunction]) is a complete lattice. For any t [member of] J, we write t [??] S = ([[??].sub.t], A).
Let L be a complete lattice with the greatest element [1.sub.L] and the least element [0.sub.L], and let (X, R) be a lattice, A [member of] [L.sup.x].
(Providence, RI) announces a new x-ray goniometry service that provides a complete lattice orientation of single crystals and is suitable for a wide variety of materials, regardless of size and weight.
We say that A is a sup-[OMEGA]-algebra if the poset (A[less than or equal to]) is a complete lattice and
From the algebraic point of view this structure forms a complete lattice, called the generalized one-sided concept lattice.
Thus, L(G, M, I) is a complete lattice and is called the concept lattice.

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