A completion-invariant extension of the concept of quasi C-continuous lattices | Zendy

Xiaojun Ruan | Zendy; Xiaoquan Xu | Zendy

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A completion-invariant extension of the concept of quasi C-continuous lattices

Author(s) -

Xiaojun Ruan,

Xiaoquan Xu

Publication year - 2017

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1708345r

Subject(s) - semilattice , mathematics , partially ordered set , lattice (music) , combinatorics , invariant (physics) , extension (predicate logic) , complete lattice , discrete mathematics , pure mathematics , computer science , condensed matter physics , mathematical physics , semigroup , physics , universality (dynamical systems) , acoustics , programming language

In this paper, the concepts of C-precontinuous posets, quasi C-precontinuous posets and meet C-precontinuous posets are introduced. The main results are: (1) A complete semilattice P is C-precontinuous(resp., quasi C-precontinuous) if and only if its normal completion is a C-continuous lattice(resp., quasi C-continuous lattice); (2) A poset is both quasi C-precontinuous and Frink quasi- continuous if and only if it is generalized completely continuous; (3) A complete semilattice is meet C-precontinuous if and only if its normal completion is meet C-continuous; (4) A poset is both quasi C-precontinuous and meet C-precontinuous if and only if it is C-precontinuous.

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