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Quasianalytic ultradifferentiability cannot be tested in lower dimensions. (English) Zbl 1434.26070

Summary: We show that, in contrast to the real analytic case, quasianalytic ultradifferentiability can never be tested in lower dimensions. Our results are based on a construction due to Jaffe.

MSC:

26E10 \(C^\infty\)-functions, quasi-analytic functions
30D60 Quasi-analytic and other classes of functions of one complex variable
46E10 Topological linear spaces of continuous, differentiable or analytic functions
58C25 Differentiable maps on manifolds
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