A note on determinacy

Bruce, J. W.; Ruas, M. A. S.; Saia, M. J.

doi:10.1090/S0002-9939-1992-1101980-7

A note on determinacy
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by J. W. Bruce, M. A. S. Ruas and M. J. Saia PDF

Proc. Amer. Math. Soc. 115 (1992), 865-871 Request permission

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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