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Abstract
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The notion of the (dual) hull-kernel topology on a collection of prime filters in a residuated lattice is introduced and investigated. It is observed that any collection of prime filters is a $T_0$ topological space under the (dual) hull-kernel topology. It is proved that any collection of prime filters is a $T_1$ space if and only if it is an antichain, and it is a Hausdorff space if and only if it satisfies some certain conditions. Some characterizations in which maximal filters form a Hausdorff space are given. In the end, we focus on the space of minimal prim filters, and verify that this space is totally disconnected Hausdorff. This paper is closed by description of the compactness of the space of the minimal prime filters using the space of prime $\alpha$-filters.
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