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Extension of Whitney Fields from Subanalytic Sets.

Edward Bierstone — 1978

Inventiones mathematicae

Semianalytic and subanalytic sets

Edward Bierstone; Pierre D. Milman — 1988

Publications Mathématiques de l'IHÉS

Arc-analytic functions.

Pierre D. Milman; Edward Bierstone — 1990

Inventiones mathematicae

Local analytic invariants

Edward Bierstone; Pierre D. Milman — 1988

Banach Center Publications

Relations among analytic functions. I

Edward Bierstone; P. D. Milman — 1987

Annales de l'institut Fourier

Neither real analytic sets nor the images of real or complex analytic mappings are, in general, coherent. Let $Φ : X \to Y$ be a morphism of real analytic spaces, and let $Ψ : 𝒢 \to ℱ$ be a homomorphism of coherent modules over the induced ring homomorphism $Φ^{*} : 𝒪_{Y} \to 𝒪_{X}$ . We conjecture that, despite the failure of coherence, certain natural discrete invariants of the modules of formal relations $ℛ_{a} = Ker {\hat{Ψ}}_{a}$ , $a \in X$ , are upper semi-continuous in the analytic Zariski topology of $X$ . We prove semicontinuity in many cases (e.g. in the algebraic category)....

Relations among analytic functions. II

Edward Bierstone; P. D. Milman — 1987

Annales de l'institut Fourier

This is a sequel to “Relations among analytic functions I”, , , fasc. 1, [pp. 187-239]. We reduce to semicontinuity of local invariants the problem of finding $𝒞^{\infty}$ solutions to systems of equations involving division and composition by analytic functions. We prove semicontinuity in several general cases : in the algebraic category, for “regular” mappings, and for module homomorphisms over a finite mapping.

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