functional analysis, two elements x and y of a vector lattice X are lattice disjoint or simply disjoint if inf { | x | , | y | } = 0 {\displaystyle \inf \left\{|x|...

{\displaystyle y} are lattice disjoint then the band generated by { x } , {\displaystyle \{x\},} contains y {\displaystyle y} and is lattice disjoint from the band...

{\displaystyle x{\text{ and }}y} in a vector lattice X {\displaystyle X} are said to be lattice disjoint or disjoint if inf { | x | , | y | } = 0 , {\displaystyle...

distributive lattices such an M is always a prime ideal. A proof of this statement follows. Proof Assume the ideal M is maximal with respect to disjointness from...

origin of the reciprocal lattice. There are also second, third, etc., Brillouin zones, corresponding to a sequence of disjoint regions (all with the same...

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...

are order-preserving homeomorphisms between these examples. For any two disjoint total orders ( A 1 , ≤ 1 ) {\displaystyle (A_{1},\leq _{1})} and ( A 2...

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...

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...