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Adjoint functors between the categories of partially
The general adjunction theorem
Special adjunction theorems for various categories
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0-distributive a a b a v b basis Boolean lattices Boolean space characteristic function compact elements compact space containing continuous function continuous map continuous retraction coreflection COROLLARY counit DEFINITION denote dense distributive lattice dLat DUALITY THEOREM finite full subcategory function f functor Spec greatest element Hausdorff hence homeomorphism implies isomorphism lattice homomorphisms lattice morphisms left adjoint LEMMA max Spec(L maximal character maximal ideals minimal morphism f neighborhood order preserving function P-character p.c.lattice 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 s.l.semigroup character satisfied semigroup semilattice separate the points Slsem Spec 0(X Spec(L SPECIAL ADJUNCTION THEOREM Specp spectral spaces Stone-Cech compactification subbasis subcategory of Top sublattice surjective theory topological space ultrafilter weakly complemented