Completely Precontinuous Posets | Zendy

Wenfeng Zhang | Zendy; Xiaoquan Xu | Zendy

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Completely Precontinuous Posets

Author(s) -

Wenfeng Zhang,

Xiaoquan Xu

Publication year - 2014

Publication title -

electronic notes in theoretical computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.242

H-Index - 60

ISSN - 1571-0661

DOI - 10.1016/j.entcs.2014.01.014

Subject(s) - partially ordered set , mathematics , combinatorics , distributive property , distributive lattice , relation (database) , lattice (music) , star product , property (philosophy) , chain (unit) , discrete mathematics , hasse diagram , pure mathematics , computer science , physics , philosophy , epistemology , database , astronomy , acoustics

In this paper, concepts of strongly way below relations, completely precontinuous posets, coprimes and Heyting posets are introduced. The main results are: (1) The strongly way below relations of completely precontinuous posets have the interpolation property; (2) A poset P is a completely precontinuous poset iff its normal completion is a completely distributive lattice; (3) An ω-chain complete P is completely precontinuous iff P and Pop are precontinuous and its normal completion is distributive iff P is precontinuous and has enough coprimes; (4) A poset P is completely precontinuous iff the strongly way below relation is the smallest approximating auxiliary relation on P iff P is a Heyting poset and there is a smallest approximating auxiliary relation on P. Finally, given a poset P and an auxiliary relation on P, we characterize those join-dense subsets of P whose strongly way-below relation agrees with the given auxiliary relation

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