Hausdorff limits of Rolle leaves

2011/07/04 by Jean-Marie Lion, Patrick Speissegger, Lion, Jean-Marie +1
Computer Science · Mathematics · #58A17 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Differential Geometry (math.DG) #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals #Primary 14P15 #Secondary 03C64 #math.DG #math.LO #msc:03C64 #msc:14P15 #msc:58A17

paper · pdf · doi:10.48550/arxiv.1107.0648

12 pages

arxiv created 2011/07/04 · openalex publication_date 2011/07/04 · arxiv updated 2011/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Topology of Definable Hausdorff Limits
• T-Convexity, Tame Extensions and Definability of Hausdorff Limits in O-minimal Structures with Generic Derivations
• Limits of definable families and dilations in nilmanifolds
• Approximation by O-minimal sets in power-bounded T-convex valued fields
• Expansions of the real field by open sets: definability versus interpretability