Y. J. Zhang - School of Mathematics and Statistics, Shaanxi Normal University, Xi&#۰۳۹;an ۷۱۰۱۱۹, P.R. China
B. Zhao - School of Mathematics and Statistics, Shaanxi Normal University, Xi&#۰۳۹;an ۷۱۰۱۱۹, 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: (۱) The set of all C-compact elements of a completeQ-ordered set is irreducible complete; (۲) The Scott Q-cotopology of a Q-ordered set under the fuzzy inclusion order is C-continuous, evenC-prealgebraic; (۳) We establish an adjunction between the category of irreducible complete Q-ordered sets and the category of C-prealgebraic complete Q-ordered sets.

category, Q-order, Scott Q-cotopology, C-continuity