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.
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