On the relative Kuo condition and the second relative Kuo condition
Abstract
The Kuo condition and the the second Kuo condition are known as criteria for an r-jet to be V-sufficient in Cr mappings and Cr+1 mappings, respectively. In a previous paper we considered the notions of V-sufficiency of jets and these Kuo conditions in the relative case to a given closed set, and showed that the relative Kuo condition is a criterion for a relative r-jet to be V-sufficient in Cr mappings and the second relative Kuo condition is a sufficient condition for a relative r-jet to be V-sufficient in Cr+1 mappings. In this paper we discuss several conditions equivalent to the relative Kuo condition or the second relative Kuo condition.
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