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.

介绍并研究了剩余格中素滤波器集合上的（双）壳核拓扑概念。可以观察到，任何素数过滤器的集合都是（双）壳核拓扑下的一个\(T_0\)拓扑空间。证明了任何素数过滤器的集合是一个\(T_1\)空间当且仅当它是一个反链，并且当且仅当它满足某些条件时它是一个Hausdorff空间。给出了一些特征，其中最大滤波器形成 Hausdorff 空间。最后，我们关注最小prim过滤器的空间，并验证这个空间是完全不连通的Hausdorff。本文通过使用质数\(\alpha \)的空间描述最小质数滤波器的空间的紧凑性来结束-过滤器。