In knowledge structure theory, the conjunctive model is the dual of the disjunctive model. What, then, is the dual of the competence model? Regarding the competence model, prior work has established necessary and sufficient conditions for delineating knowledge spaces via the competence model and has well studied the fringe characterization of knowledge states in delineated knowledge spaces. Accordingly, what are the necessary and sufficient conditions for delineating simple closure spaces via the competence model? How can the fringe of knowledge states be characterized in delineated simple closure spaces? Furthermore, in the competence model, top space characterization is complex. How to simplify it? To address these problems, this paper proposes the dual skill function (i.e., dual competence model) and the complement skill function. The dual competence model provides a novel methodology for analyzing the competence model, enabling the transfer of results on delineated knowledge spaces to their dual closure spaces, and offering a more direct characterization of top spaces. In doing so, it effectively addresses the latter three problems. These results refine knowledge structure theory.