<p>In this paper, we consider the set of all proper filters of a residuated lattice, equipped with the coarse lower topology. We study some topological properties of this space and we show that this space is spectral. Then after introducing a family of proper filters that satisfies the avoidance property, meaning that if a filter is included in the union of the family, then it is included in some member of the family, we show that a family of proper filters satisfies the avoidance property if and only if it is quasi-compact in the coarse lower topology. Moreover, by providing related examples and results, we construct families with this property. Finally, we show that the avoidance property does not necessarily hold for the family of minimal prime filters of a residuated lattice. As an application of this concept, by characterizing residuated lattices whose family of minimal prime filters satisfies the avoidance property, we prove that a residuated lattice is quasi-complemented if and only if the family of its minimal prime filters satisfies the avoidance property. Several further related results are also derived.</p>