## A Compendium of Continuous Lattices |

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### Contents

A Primer of Complete Lattices | 1 |

Morphisms into chains | 2 |

Projective limits and functors which preserve them | 3 |

Copyright | |

36 other sections not shown

### Other editions - View all

A Compendium of Continuous Lattices G. Gierz,K. H. Hofmann,K. Keimel,J. D. Lawson,M. Mislove,D. S. Scott Limited preview - 2012 |

A Compendium of Continuous Lattices G. Gierz,K. H. Hofmann,K. Keimel,J. D. Lawson,M. Mislove,D. S. Scott No preview available - 1980 |

### Common terms and phrases

adjoint algebraic lattices apply assume basis bound called Chapter characterization Clearly closed compact complete lattice conclude consider construction contained continuous lattice convergence COROLLARY define definition denote directed set discussion element equivalent example EXERCISE exists fact filter finite following statements function functor given gives Hausdorff Hence Heyting algebra Hofmann holds homomorphism ideal implies important injective interpolation property intersection interval irreducible isomorphism Lawson topology LEMMA limit lower sets maximal means meet meet-continuous lattices monotone morphisms natural neighborhood open sets particular poset preserves preserves arbitrary preserves directed sups prime projective Proof PROPOSITION prove recall relation Remark respect satisfies Scott topology Scott-open semilattice sober space Spec subset sup-semilattice Suppose Theorem theory topological semilattice topological space ultrafilter unit upper set whence