A Representation of all Tolerances on a Set by Certain Type of Covers

Most of the correspondences, especially those in Computer Science, and Mathematics which are not a Galois correspondence are actually Lagois correspondences introduced by Austin Melton. In this paper we represent the poset of all tolerances on any set, including the infinite ones, by certain type of covers on the same via a Lagois correspondence in such a way that it is a natural extension of the complete isomorphism between the set of all partitions of a non empty set and the set of all equivalence relations on the same set.