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A characterization of $ C\sp{\infty }$-sufficient $ k$-jets


Author: Wojciech Kucharz
Journal: Proc. Amer. Math. Soc. 55 (1976), 419-423
MSC: Primary 58C25
MathSciNet review: 0400291
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Abstract: We improve some results of Mather and Arnold and find several necessary and sufficient conditions of sufficiency of $ k$-jets. As a corollary we prove that the set of $ {C^\infty }$-sufficient $ k$-jets is a semialgebraic subset of the space of $ k$-jets of $ {C^\infty }$ mappings $ F:({R^n},0) \to (R,0)$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0400291-3
Keywords: $ k$-jets of $ {C^\infty }$ mappings
Article copyright: © Copyright 1976 American Mathematical Society