O-minimal structures provide a tame setting for real geometry, where every definable set has finitely many connected components and behaves nicely. A natural operation is to take a family of definable sets parameterized by a variable and ask what happens in the geometric limit, specifically the Hausdorff limit, as the parameter approaches a boundary value. The open problem is to characterize precisely which o-minimal structures are closed under this Hausdorff limit operation for definable families, meaning the limit set is again definable in the same structure rather than requiring new primitives or an expansion.