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The notion of a (semi)topological residuated lattice is introduced and its properties are investigated. Some separation axioms on topological residuated lattices are studied. The notion of completion of a residuated lattice is introduced and characterized by means of the inverse limit of an inverse system. A residuated lattice with a given system of filters is illustrated with the linear topology and it is shown that a compact and Hausdorff residuated lattice with the linear topology is complete.
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