Abstract
By means of closure systems and closure operators on complete lattices, a generalized convex structure under which classical convex structures and L-convex structures are consistent with each other is established. The related convex spaces and hull spaces are investigated, and it is shown that they are isomorphic to each other from the viewpoint of category. In order to further characterize this convex structure, the notion of enclosed order spaces and their corresponding mappings are introduced. It is proved that the category of enclosed order spaces is also isomorphic to that of convex spaces we presented.
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