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arXiv · alg-geom/9506001

Composite Differentiable Functions

Edward Bierstone·Pierre D. Milman·Wieslaw Pawlucki
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Abstract

We introduce a new point of view towards Glaeser's theorem on composite $C^\infty$ functions [Ann. of Math. 1963], with respect to which we can formulate a ``$C^k$ composite function property" that is satisfied by all semiproper real analytic mappings. As a consequence, we see that a closed subanalytic set $X$ satisfies the $C^\infty$ composite function property if and only if the ring $C^\infty (X)$ of $C^\infty$ functions on $X$ is the intersection of all finite differentiability classes.

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BibTeXRIS

Edward Bierstone, Pierre D. Milman, Wieslaw Pawlucki. 1995-06-01. Composite Differentiable Functions. https://arxiv.org/abs/alg-geom/9506001

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