This paper concerns the porosity of the class \({\cal D}\) of diametrically complete sets, as a subset of the metric space of closed, convex bounded sets \({\cal H}\) endowed with the Hausdorff metric in Banach spaces. We begin by answering in the negative a question posed in [7] regarding the existence of non-trivial diametrically minimal sets in non-reflexive Banach spaces. This result is then used to prove that, if dim X > 1 and Jung’s constant J(X) < 2, \({\cal D}\) is uniformly very porous. Our lower bound for the extreme porosity of \({\cal D}\) at each element of \({\cal H}\) depends uniquely on J(X). When dim X > 1 and the smaller class \({\cal W}\) of constant width sets is considered, we prove the existence of a universal lower bound for its extreme porosity.

本文涉及直径完全集的类\（{\ cal D} \）的孔隙度，它是具有Hausdorff度量的封闭凸集有界集\（{\ cal H} \）度量空间的一个子集Banach空间。我们首先以否定的方式回答[7]中提出的有关非自反Banach空间中非平凡最小集的存在的问题。然后使用该结果证明，如果dim X > 1并且Jung常数J（X）<2，\（{\ cal D} \）均匀地非常多孔。我们的下界的极端孔隙率\（{\ CAL d} \）在的每个元素\（{\ CAL H} \）唯一地取决于Ĵ（X）。当考虑Dim X > 1并考虑恒定宽度集的较小类\（{\ cal W} \）时，我们证明了存在其极限孔隙度的通用下界。