C-continuous fuzzy posets

Document Type : Research Paper


School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, P.R. China


In this paper, we develop the C-continuity via Scott Q-cotopological spaces, where Q is a commutative and integral quantale.
The main results are: (1) The set of all C-compact elements of a complete
Q-ordered set is irreducible complete; (2) The Scott Q-cotopology
of a Q-ordered set under the fuzzy inclusion order is C-continuous, even
C-prealgebraic; (3) We establish an adjunction between the category of irreducible complete Q-ordered sets and the category of C-prealgebraic complete Q-ordered sets.