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	ProofOfSquareRootOfSquareRootBinomial proof of square root of square root binomial ProofOfSteinersTheorem proof of Steiner’s theorem ProofOfStewartsTheorem proof of Stewart’s theorem ProofOfStirlingsApproximation proof of Stirling’s approximation ProofOfStolzCesaroTheorem Proof of Stolz-Cesaro theorem ProofOfStoneWeierstrassTheorem proof of Stone-Weierstrass theorem ProofOfSumRule proof of sum rule ProofOfTangentsLaw proof of tangents law ProofOfTaubersConvergenceTheorem proof of Tauber’s convergence theorem ProofOfTaylorsFormulaForMatrixFunctions ProofOfTaylorsTheorem proof of Taylor’s formula for matrix functions proof of Taylor’s Theorem ProofOfThalesTheorem proof of Thales’ theorem ProofOfTheBurnsideBasisTheorem