## A general character theory for partially ordered sets and lattices, Issues 122-123 |

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0-distributive a a b a v b basis bijection Boolean lattices Boolean space characteristic function compact space containing continuous characters continuous function continuous map coreflection COROLLARY counit DEFINITION denote dense distributive lattice dLat DUALITY THEOREM finite full subcategory functor Spec greatest element Hausdorff hence homeomorphism implies initial section injective iff isomorphism lattice homomorphisms lattice morphisms left adjoint LEMMA max Spec(L maximal character maximal ideals minimal morphism f open sets order preserving function P-character p.c.lattice p.o.semigroup p.o.set partially ordered sets Posem Poset prime elements prime filter prime ideal projective cover Proof PROPOSITION pseudocomplemented lattice quasi-Boolean space quasicompact open sets quasicompact open subsets quasicompact sets quasiproper quotient map regular character resp satisfied semigroup semilattice separate the points Slsem Spec 0(X Spec_ Spec(L SPECIAL ADJUNCTION THEOREM Specp spectral spaces Stone-Cech compactification subbasis subcategory of Top sublattice surjective Top whose objects topological space ultrafilter weakly complemented