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On the semigroup of Ck selfmaps of Rn

Published online by Cambridge University Press:  09 April 2009

G. R. Wood
G. R. Wood
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT 2600.
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Magill, Jr. and Yamamuro have been responsible in recent years for a number of papers showing that the property that every automorphism is inner is held by many semigroups of functions and relations on topological spaces. Following [9], we say a semigroup has the Magill property if every automorphism is inner. we say a semigroup has the Magill property if every automorphism is inner. That the semigroup of Fréchet differentiable selfmaps, D of a finite dimensional Banach space E, had the Magill property was shown in [10], while a lengthy result in [6] extended this to the semigroup of k times Fréchet differentiable selfmaps, Dk, of a Fréchet Montel space (FM-space). In the latter paper it was noted that with a little additional effort the semigroup Ck, of k times continuously Fréchet differentiable selfmaps of FM-space, could be shown to possess the Magill property. It is the purpose of this paper to present a simpler proof of this result in the case where the underlying space is finite dimensional.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 17 , Issue 4 , June 1974 , pp. 389 - 393
Copyright
Copyright © Australian Mathematical Society 1974

References

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