complete lattice homomorphism

Complete lattice homomorphism is a function from one lattice to an other lattice, which preserves arbitrary (not only finite) meets and joins.

If $\\phi:L\\to M$ is lattice homomorphism between complete lattices $L$ and $M$ such that

•
$\\phi(\\bigvee\\{a_{i}\\mid i\\in I\\})=\\bigvee\\{\\phi(a_{i})\\mid i\\in I\\}$ , and
•
$\\phi(\\bigwedge\\{a_{i}\\mid i\\in I\\})=\\bigwedge\\{\\phi(a_{i})\\mid i\\in I\\}$ ,

then $\\phi$ is called a complete lattice homomorphism.

Most often are considered complete lattice homomorphisms from one complete lattice to an other complete lattice (that is when all meets and joins are defined).

Complete lattice homomorphism is a special case of lattice homomorphism.

单词	CompleteLatticeHomomorphism
释义	complete lattice homomorphism Complete lattice homomorphism is a function from one lattice to an other lattice, which preserves arbitrary (not only finite) meets and joins. If $\\phi:L\\to M$ is lattice homomorphism between complete lattices $L$ and $M$ such that • $\\phi(\\bigvee\\{a_{i}\\mid i\\in I\\})=\\bigvee\\{\\phi(a_{i})\\mid i\\in I\\}$ , and • $\\phi(\\bigwedge\\{a_{i}\\mid i\\in I\\})=\\bigwedge\\{\\phi(a_{i})\\mid i\\in I\\}$ , then $\\phi$ is called a complete lattice homomorphism. Most often are considered complete lattice homomorphisms from one complete lattice to an other complete lattice (that is when all meets and joins are defined). Complete lattice homomorphism is a special case of lattice homomorphism.
随便看	dual of Dilworth’s theorem DualOfStoneRepresentationTheorem dual of Stone representation theorem DualSpace dual space DualSpaceOfABooleanAlgebra dual space of a Boolean algebra DualSpaceSeparatesPoints dual space separates points DulacsCriteria DulacsTheorem Dulac’s criteria Dulac’s theorem DunklWilliamsInequality Dunkl-Williams inequality Duodecimal duodecimal DusaMcDuff Dusa McDuff DyadProduct dyad product DyckLanguage Dyck language DynamicalSystem dynamical system