Hausdorff limits of Rolle leaves

Let $${\mathcal{R}}$$ be an o-minimal expansion of the real field. We introduce a class of Hausdorff limits, the T∞-limits over $${\mathcal{R}}$$, that do not in general fall under the scope of Marker and Steinhorn’s definability-of-types theorem. We prove that if $${\mathcal{R}}$$ admits analytic cell decomposition, then every T∞-limit over $${\mathcal{R}}$$ is definable in the pfaffian closure of $${\mathcal{R}}$$.