Complemented Lattice

up:: Lattice

A Limited Lattice $(X,\wedge ,\vee )$ is said to be a complemented lattice if any points $x\in X$ have at least one complement in $X$, such that¹

$$(x\wedge y=0)\wedge (x\vee y=1)$$

Properties

Every distributive and limited lattice has unique complements

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References

Footnotes

1. Yes, I’m using $\wedge$ as the logical “and”, as well as the join operator. ↩