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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Piecewise linearization of real-valued subanalytic functions


Author: Masahiro Shiota
Journal: Trans. Amer. Math. Soc. 312 (1989), 663-679
MSC: Primary 32B25; Secondary 32B20
MathSciNet review: 958902
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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 :\vert K\vert \to X$) such that $ f \circ \pi {\vert _\sigma }, \sigma \in K$, are linear.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0958902-3
PII: S 0002-9947(1989)0958902-3
Keywords: Subanalytic set, triangulation, $ {\text{PL}}$ function
Article copyright: © Copyright 1989 American Mathematical Society