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2 results

  • Constructive Complete Distributivity III

  • Robert Rosebrugh, R. J. Wood
  • Journal:
    Canadian Mathematical Bulletin / Volume 35 / Issue 4 / 01 December 1992
    Published online by Cambridge University Press:
    20 November 2018, pp. 537-547
    Print publication:
    01 December 1992
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  • A complete lattice L is constructively completely distributive,(CCD)(L), if the sup map defined on down closed subobjects has a left adjoint. We characterize preservation of this property by left exact functors between toposes using a "logical comparison transformation". The characterization is applied to (direct images of) geometric morphisms to show that local homeomorphisms (in particular, product functors) preserve (CCD) objects, while preserving (CCD) objects implies openness.

  • Metrizability Conditions for Completely Distributive Lattices

  • G. Gierz, J. D. Lawson, A. R. Stralka
  • Journal:
    Canadian Mathematical Bulletin / Volume 26 / Issue 4 / 01 December 1983
    Published online by Cambridge University Press:
    20 November 2018, pp. 446-453
    Print publication:
    01 December 1983
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  • A lattice is said to be essentially metrizable if it is an essential extension of a countable lattice. The main result of this paper is that for a completely distributive lattice the following conditions are equivalent: (1) the interval topology on L is metrizable, (2) L is essentially metrizable, (3) L has a doubly ordergenerating sublattice, (4) L is an essential extension of a countable chain.