## Distributive lattices |

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### Contents

Ordinals and cardinals | 1-3 |

Direct products 8 | 1-5 |

Congruence relations 9 | 1-6 |

Copyright | |

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### Common terms and phrases

a-complete a-representable algebra of order atoms Boolean space characterization class of algebras compact open complete Boolean algebra complete distributive lattice complete lattice congruence relation contradiction coproduct Corollary countable defined Definition denote Dwinger element embedding epic epimorphism equational category equational class equational subclasses Exercise finite follows from Theorem free algebras free Boolean extension functor Gratzer Hence Heyting algebra homomorphism hypothesis identity implies injective isomorphic join irreducible Lemma Let Lbea Lukasiewicz algebras Math monic monomorphisms Morgan algebra morphism n-chain normal completion Note one-one open sets ordinal partially ordered poset Post algebra preserves prime ideal proof of Theorem Prove pseudocomplemented distributive lattice relatively complemented retract ring of sets satisfies Section Sf(L Stone algebra Stone space subalgebra subdirect product subdirectly irreducible sublattice Suppose topological weakly projective X,es