Verdier stratifications and [wf]-stratification in o-minimal structures

1997/04/14 by Ta Lê Loi, Loi, Ta Lê
Mathematics · #Advanced Topology and Set Theory #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.DG

paper · pdf · doi:10.48550/arxiv.math/9704232

arxiv created 1997/04/14 · openalex publication_date 1997/04/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the existence of Verdier stratifications for sets definable in any o-minimal structure on (R, +, .). It is also shown that the Verdier condition (w) implies the Whitney condition (b) in o-minimal structures on (R, +, .). As a consequence the Whitney Stratification Theorem holds. The existence of (wf)-stratification of functions definable in polynomially bounded o-minimal structures is presented.

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