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New proofs of some theorems on infinitely differentiable functions

Published online by Cambridge University Press:  17 April 2009

Michael A. B. Deakin
Michael A. B. Deakin
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria.
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New proofs are given for the splitting lemma and two of Mather's theorems in the theory of C∞-functions. They use a Taylor series approach rather than the usual map-germ theory and are more elementary than previous proofs. A geometric characterisation of a class of degenerate functions is proved to hold in this account but not in the usual framework.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 17 , Issue 2 , October 1977 , pp. 161 - 175
Copyright
Copyright © Australian Mathematical Society 1977

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