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- W4301511099 abstract "We prove that a theorem of Pawlucki, showing that Whitney regularity for a subanalytic set with a smooth singular locus of codimension one implies the set is a finite union of differentiable manifolds with boundary, applies to definable sets in polynomially bounded o-minimal structures. We give a refined version of Pawlucki's theorem for arbitrary o-minimal structures, replacing Whitney (b)-regularity by a quantified version, and we prove related results concerning normal cones and continuity of the density. We analyse two counterexamples to the extension of Pawlucki's theorem to definable sets in general o-minimal structures, and to several other statements valid for subanalytic sets. In particular we give the first example of a Whitney (b)-regular definably stratified set for which the density is not continuous along a stratum." @default.
- W4301511099 created "2022-10-05" @default.
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- W4301511099 date "2017-01-18" @default.
- W4301511099 modified "2023-09-27" @default.
- W4301511099 title "On the local geometry of definably stratified sets" @default.
- W4301511099 doi "https://doi.org/10.48550/arxiv.1701.05087" @default.
- W4301511099 hasPublicationYear "2017" @default.
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