Priestley Spaces, Quasi–hyperalgebraic Lattices and Smyth Powerdomains

Yang, Jinmeng; Luo, Mao

doi:10.1007/s10114-005-0737-8

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Cited by 4 publications

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“…The condition (4) in the above theorem is called the intrinsic characterization of hyperalgebraic lattices, which is first obtained in [11].…”

Section: Topological Representations For Distributive Hyperalgebraic mentioning

confidence: 99%

Topological representations of distributive hypercontinuous lattices

Yang

2009

Chin. Ann. Math. Ser. B

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The concept of locally strong compactness on domains is generalized to general topological spaces. It is proved that for each distributive hypercontinuous lattice L, the space SpecL of nonunit prime elements endowed with the hull-kernel topology is locally strongly compact, and for each locally strongly compact space X, the complete lattice of all open sets O(X) is distributive hypercontinuous. For the case of distributive hyperalgebraic lattices, the similar result is given. For a sober space X, it is shown that there is an order reversing isomorphism between the set of upper-open filters of the lattice O(X) of open subsets of X and the set of strongly compact saturated subsets of X, which is analogous to the well-known Hofmann-Mislove Theorem.

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“…The condition (4) in the above theorem is called the intrinsic characterization of hyperalgebraic lattices, which is first obtained in [11].…”

Section: Topological Representations For Distributive Hyperalgebraic mentioning

confidence: 99%