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Differentiable retracts and a modified inverse function theorem

Published online by Cambridge University Press:  17 April 2009

W. Barit  and
G.R. Wood
W. Barit
Affiliation:
Department of Mathematics, University of Canterbury, Christchurch, New Zealand.
G.R. Wood
Affiliation:
Department of Mathematics, University of Canterbury, Christchurch, New Zealand.
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Abstract

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A lemma is presented which is a weak version of the inverse function theorem, in that differentiability is assumed instead of continuous differentiability. The result holds only for finite dimensional spaces; a counter-example is given for the infinite dimensional analogue. The lemma is used to answer a question posed by Nadler concerning differentiable retracts.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 18 , Issue 1 , February 1978 , pp. 37 - 43
Copyright
Copyright © Australian Mathematical Society 1978

References

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