lattice of sets
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Lattice (order) — See also: Lattice (group) The name lattice is suggested by the form of the Hasse diagram depicting it. Shown here is the lattice of partitions of a four element set {1,2,3,4}, ordered by the relation is a refinement of . In mathematics, a… … Wikipedia
Lattice (group) — A lattice in the Euclidean plane. In mathematics, especially in geometry and group theory, a lattice in Rn is a discrete subgroup of Rn which spans the real vector space Rn. Every lattice in Rn … Wikipedia
Lattice (discrete subgroup) — In Lie theory and related areas of mathematics, a lattice in a locally compact topological group is a discrete subgroup with the property that the quotient space has finite invariant measure. In the special case of subgroups of R n , this amounts … Wikipedia
lattice — UK [ˈlætɪs] / US noun [countable] Word forms lattice : singular lattice plural lattices 1) a structure consisting of narrow pieces of wood, plastic, metal etc crossed over each other with spaces between them vines twining round a lattice 2) a… … English dictionary
lattice — lat|tice [ lætıs ] noun count 1. ) a structure consisting of narrow pieces of wood, plastic, metal, etc. crossed over each other with spaces between them: vines twining around a lattice 2. ) a pattern or shape with sets of parallel lines that… … Usage of the words and phrases in modern English
Distributive lattice — In mathematics, distributive lattices are lattices for which the operations of join and meet distribute over each other. The prototypical examples of such structures are collections of sets for which the lattice operations can be given by set… … Wikipedia
Complete lattice — In mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum (join) and an infimum (meet). Complete lattices appear in many applications in mathematics and computer science. Being a special instance of… … Wikipedia
Union-closed sets conjecture — In combinatorial mathematics, the union closed sets conjecture is an elementary problem, posed by Péter Frankl in 1979 and still open as of 2008. A family of sets is said to be union closed if the union of any two sets from the family remains in… … Wikipedia
Hexagonal lattice — The hexagonal lattice or equilateral triangular lattice is one of the five 2D lattice types.Three nearby points form an equilateral triangle. In images four orientations of such a triangle are by far the most common. They can conveniently be… … Wikipedia
Free lattice — In mathematics, in the area of order theory, a free lattice is the free object corresponding to a lattice. As free objects, they have the universal property. The word problem for free lattices is also challenging.Formal definitionAny set X may be … Wikipedia
Completely distributive lattice — In the mathematical area of order theory, a completely distributive lattice is a complete lattice in which arbitrary joins distribute over arbitrary meets. Formally, a complete lattice L is said to be completely distributive if, for any doubly… … Wikipedia
