Meet Precontinuous Posets | Zendy

Wenfeng Zhang | Zendy; Xiaoquan Xu | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Meet 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.2014.01.015

Subject(s) - partially ordered set , mathematics , relation (database) , combinatorics , lattice (music) , star product , generalization , discrete mathematics , complete lattice , computer science , data mining , physics , mathematical analysis , universality (dynamical systems) , quantum mechanics , acoustics

In this paper, we introduce the concept of meet precontinuous posets, a generalization of meet continuous lattices to posets. The main results are: (1) A poset P is meet precontinuous iff its normal completion is a meet continuous lattice iff a certain system γ(P) which is, in the case of complete lattices, the lattice of all Scott-closed sets is a complete Heyting algebra; (2) A poset P is precontinuous iff the way below relation is the smallest approximating auxiliary relation iff P is meet precontinuous 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 way-below relation agrees with the given auxiliary relation

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research