In mathematics, specifically in order theory and functional analysis, two elements x and y of a vector lattice X are lattice disjoint or simply disjoint if , in which case we write , where the absolute value of x is defined to be .[1]
We say that two sets A and B are lattice disjoint or disjoint if a and b are disjoint for all a in A and all b in B, in which case we write .[2]
If A is the singleton set then we will write in place of .
For any set A, we define the disjoint complement to be the set .[2]
functional analysis, two elements x and y of a vector lattice X are latticedisjoint or simply disjoint if inf { | x | , | y | } = 0 {\displaystyle \inf \left\{|x|...
{\displaystyle x{\text{ and }}y} in a vector lattice X {\displaystyle X} are said to be latticedisjoint or disjoint if inf { | x | , | y | } = 0 , {\displaystyle...
origin of the reciprocal lattice. There are also second, third, etc., Brillouin zones, corresponding to a sequence of disjoint regions (all with the same...
{\displaystyle y} are latticedisjoint then the band generated by { x } , {\displaystyle \{x\},} contains y {\displaystyle y} and is latticedisjoint from the band...
exactly one of these subsets (i.e., the subsets are nonempty mutually disjoint sets). Equivalently, a family of sets P is a partition of X if and only...
the same as the intersection graph of the sets from the family. The disjointness graph of G, denoted D(G), is constructed in the following way: for each...
are order-preserving homeomorphisms between these examples. For any two disjoint total orders ( A 1 , ≤ 1 ) {\displaystyle (A_{1},\leq _{1})} and ( A 2...
number triangle. A partition of a set S is a set of non-empty, pairwise disjoint subsets of S, called "parts" or "blocks", whose union is all of S. Consider...
but does not contain the empty set, this is simply a family of pairwise disjoint sets. A strong upwards antichain B is a subset of P in which no two distinct...
Each equivalence relation provides a partition of the underlying set into disjoint equivalence classes. Two elements of the given set are equivalent to each...
degrees on each axis. The problem of finding the smallest ball such that k disjoint open unit balls may be packed inside it has a simple and complete answer...
algebra, a skew lattice is an algebraic structure that is a non-commutative generalization of a lattice. While the term skew lattice can be used to refer...
n} -element set. Since the lattices of flats of matroids are exactly the geometric lattices, this implies that the lattice of partitions is also geometric...
inclusion ( ⊆ {\displaystyle \subseteq } ), each relation has a place in the lattice of subsets of X × Y . {\displaystyle X\times Y.} A binary relation is called...
partially ordered sets, a finite simple matroid is equivalent to a geometric lattice. Matroid theory borrows extensively from the terms used in both linear...
Fuzzy sets are disjoint if and only if their supports are disjoint according to the standard definition for crisp sets. For disjoint fuzzy sets A , B...
others to invest their time, energy, and careers into the effort. The term lattice organization for an organization using open allocation was coined by Bill...
1 n C i {\displaystyle A\setminus B=\bigcup _{i=1}^{n}C_{i}} for some disjoint C 1 , … , C n ∈ S . {\displaystyle C_{1},\ldots ,C_{n}\in {\mathcal {S}}...
{\displaystyle g\geq 0} then f {\displaystyle f} and g {\displaystyle g} are latticedisjoint if and only if for each x ≥ 0 {\displaystyle x\geq 0} and real r >...
instead of fields. A Dowling lattice is the geometric lattice of flats associated with a Dowling geometry. The lattice and the geometry are mathematically...
length two are transpositions. Two cycles are disjoint if they have disjoint subsets of elements. Disjoint cycles commute: for example, in S6 there is the...
an interval Partition of a set Ordered partition Partition refinement Disjoint-set data structure Partition problem 3-partition problem Partition topology...
following theorem: For any distributive lattice L, if an ideal I is maximal among all ideals of L that are disjoint to a given filter F, then I is a prime...
an orthocomplemented lattice. Quantum-mechanical observables and states can be defined in terms of functions on or to the lattice, giving an alternate...
of Z 3 4 {\displaystyle \mathbb {Z} _{3}^{4}} can be partitioned into disjoint cap sets. They reported that it is possible to use four different cap sets...
example, +2. 3. Sometimes used instead of ⊔ {\displaystyle \sqcup } for a disjoint union of sets. - (minus sign) 1. Denotes subtraction and is read as...
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