A Completion-Invariant Extension of the Concept of Quasi C-continuous Lattices

Abstract

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.