1. In AIPS++, an abstract base class which presents an interface to a finite-volume, linear, rectangular, or hyper-rectangular structure. The Lattice is fundamentally described by its shape. 2. In domain theory partially ordered set in which all finite subsets have a least upper bound and greatest lower bound.

A structure defined by a partial order where the points in the structure are connected by lines, and being connected by a line means that the higher element is "greater" than the lower element. The lattice will often have a top element which is greater than any other element in the set, and a corresponding bottom element which is less than any other element in the set.

A sequence of accelerator elements, often periodic, used to focus, accelerate, and bend a beam.

A partially ordered set for which every pair of elements has a greatest lower bound and a least upper bound.

a CPO where the LUB and GLB of any pair of elements exist

a finite set together with a partial ordering on its elements such that for every pair of elements there is a least upper bound and a greatest lower bound

a mathematical object that, like a set, contains elements

a partially ordered set in which any two elements have a greatest lower bound and a least upper bound

a partial ordering of a set under a relation where all finite subsets have a least upper bound and a greatest lower bound

a partial order where for each pair of elements x and y, the least upper bound and greatest lower bound of x and y both always exist

a set of elements, with two binary operations which are idempotent, commutative, and associative, and which satisfy the absorption law

a set of values along with two operators (meet, join, and two unique elements, top and bottom) that satisfy certain mathematical properties

a structure consisting of a set L , a partial ordering , and two dyadic operators and

A lattice is a poset in which all non-empty finite joins (suprema) and meets (infima) exist.

In mathematics, a lattice is a partially ordered set (or poset) whose nonempty finite subsets all have a unique supremum (called join) and an infimum (called meet). Lattices can also be characterized as algebraic structures satisfying certain axiomatic identities. Since the two definitions are equivalent, lattice theory draws on both order theory and universal algebra.