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