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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A note on determinacy


Authors: J. W. Bruce, M. A. S. Ruas and M. J. Saia
Journal: Proc. Amer. Math. Soc. 115 (1992), 865-871
MSC: Primary 58C27
DOI: https://doi.org/10.1090/S0002-9939-1992-1101980-7
MathSciNet review: 1101980
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Abstract: In this paper, we present a particularly simple and direct proof that the set of noncontact-sufficient ( $ \mathcal{K}$-sufficient) germs are of infinite codimension. Our proof gives, for each $ k$, an integer $ r$ with the property that almost all $ r$-jets over any $ k$-jet $ z$ is $ \mathcal{K}$-sufficient. Similar results are obtained for $ \mathcal{A}$ or right-left equivalence when the source and target dimensions $ (n,p)$ are (2,2) and (2,3).


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DOI: https://doi.org/10.1090/S0002-9939-1992-1101980-7
Article copyright: © Copyright 1992 American Mathematical Society