A NEW APPROACH TO INTERVAL OPERATORS IN L-CONVEX SPACES

In this paper, a new type of L-interval operators is introduced. In order to characterize the relationships between L-interval operators and (arity 2) L-convex structures, the notion of L-remotehood systems is proposed. By means of L-remotehood systems, it is shown that there is a Galois correspondence between the category of L-interval spaces and that of L-convex spaces. In particular, the category of arity 2 L-convex spaces can be reflectively embedded into that of L-interval spaces.