A proof of Kurdyka's conjecture on arc-analytic functions
classification
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keywords
semialgebraicarc-analyticarc-symmetricconjecturefunctionskurdykacorrespondenceevery
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We prove a conjecture of Kurdyka stating that every arc-symmetric semialgebraic set is precisely the zero locus of an arc-analytic semialgebraic function. This implies, in particular, that arc-symmetric semialgebraic sets are in one-to-one correspondence with radical ideals of the ring of arc-analytic semialgebraic functions.
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