Extension of P-adic Definable Lipschitz Functions
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چکیده
Write OK for the valuation ting, MK for the maximal ideal of K and kK for the residue field. Let us fix $ some uniformizer of K. We denote by acm : K → OK/(MK) the map sending some nonzero x ∈ K to x$−ord(x) mod MK , and sending zero to zero. This is a definable map. We denote by RV the union of K×/(1 +MK) and {0} and by rv : K → RV the quotient map. More generally, if m ∈ N∗, we set RVm = K×/(1 +MK) ∪ {0} and rvm : K → RVm the quotient map. For m,n > 0 ∈ N, we set Qm,n = {x ∈ K× ∣∣ ord(x) ∈ nZ and acm(x) = 1}.
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