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Approximation of subanalytic sets by normal cones
Author(s) -
Ferrarotti M.,
Fortuna E.,
Wilson L.
Publication year - 2007
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdl034
Subject(s) - mathematics , submanifold , equivalence (formal languages) , invariant (physics) , stratification (seeds) , pure mathematics , stratum , cone (formal languages) , mathematical analysis , combinatorics , mathematical physics , algorithm , seed dormancy , paleontology , botany , germination , dormancy , biology
Abstract In this paper, a notion of ‘approximation of order s ’ (called ‘ s ‐equivalence’) between two closed subanalytic subsets of ℝ n along a common submanifold is introduced. It is proved that the normal cone N X ( A ) to A along X is 1‐equivalent to A along X , assuming that X is a stratum of a stratification of A satisfying Verdier's condition ( w ). Furthermore, the normal cone is shown to be a complete invariant for the classes of 1‐equivalence of subanalytic sets along a common stratum.