Abstract
Two subanalytic subsets of are called -equivalent at a common point if the Hausdorff distance between their intersections with the sphere centered at of radius vanishes to order as tends to . We strengthen this notion in the case of real subanalytic subsets of with isolated singular points, introducing the notion of tangential -equivalence at a common singular point, which considers also the distance between the tangent planes to the sets near the point. We prove that, if is the zero set of an analytic map and if we assume that has an isolated singularity, say at the origin , then for any the truncation of the Taylor series of of sufficiently high order defines an algebraic set with isolated singularity at which is tangentially -equivalent to .
Citation
Massimo Ferrarotti. Elisabetta Fortuna. Leslie Wilson. "Tangential approximation of analytic sets." Rocky Mountain J. Math. 50 (1) 125 - 133, Febuary 2020. https://doi.org/10.1216/rmj.2020.50.125
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