Realisations of Non v-Sufficient Jets with value in Rp, p > 1

The purpose of this paper is to show that if a jet cue oJ^r(n,p), n p, p > 1, is not v-sufficient in C^r+1, there existsan infinite sequence (f_i)_iN^* of realisations of o with mutuallynon-homeomorphic germs of varieties . Bochnak and Kuo [2, 5] showed it when p = 1 and thought thatthe same argument slightly modified can be used in the casep 2 [7, p. 225]. But when n p + 2, p > 1, we have to proceeddifferently. Moreover, it is necessary to prove separately theresult when n = p and n = p + 1. About C⁰-sufriciency and p> 1, Brodersen [3, p. 168] showed a similar theorem.