New proofs of some theorems on infinitely differentiable functions
- 1 October 1977
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 17 (2) , 161-175
- https://doi.org/10.1017/s0004972700010406
Abstract
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.Keywords
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