  The notion of 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 hull-kernel
and the dual hull-kernel topologies. 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 a certain condition. Some
characterizations in which maximal filters forms a Hausdorff space are given.
At the end, it is focused on the space of minimal prim filters, and it is shown
that this space is a totally disconnected Hausdorff space. This paper is closed
by a discussion abut the various forms of compactness and connectedness of this
space.
