In this paper, the notions of L-internal relations and L-enclosed relations are introduced. They are respectively defined to be crisp relations on LX satisfying a set of axioms, which can be used to characterize L-topologies. It is shown that the category of L-internal relation spaces, the category of L-enclosed relation spaces and the category of L-topological spaces are isomorphic. Moreover, the relationships among L-internal relations, L-enclosed relations and the axioms of separation are investigated.
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