Piecewise linearization of real-valued subanalytic functions

Shiota, Masahiro

doi:10.1090/S0002-9947-1989-0958902-3

Piecewise linearization of real-valued subanalytic functions
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Trans. Amer. Math. Soc. 312 (1989), 663-679 Request permission

Abstract:

We show that for a subanalytic function $f$ on a locally compact subanalytic set $X$ there exists a unique subanalytic triangulation (a simplicial complex $K$, a subanalytic homeomorphism $\pi :|K| \to X$) such that $f \circ \pi {|_\sigma }, \sigma \in K$, are linear.

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Sur la triangulation des morphismes sous-analytic