Some results on Kronecker, Dirichlet and Helson sets
Annales de l'Institut Fourier, Tome 20 (1970) no. 2, pp. 219-324.

On construit les ensembles suivants : un ensemble parfait non de Dirichlet tel que tout sous-ensemble strict fermé soit un ensemble de Kronecker ; un ensemble de Kronecker faible qui n’est pas un ensemble de type R ; un ensemble de Dirichlet dénombrable indépendant qui n’est pas un ensemble de Kronecker ; une famille de q ensembles de Kronecker disjoints dont l’union est indépendante mais n’est pas un ensemble de Helson 1/q ; une famille dénombrable d’ensembles de Kronecker disjoints dont l’union est fermée et indépendante mais n’est pas un ensemble de Helson : un ensemble de Dirichlet indépendant et parfait qui n’est pas un ensemble de Helson.

We construct the following: a perfect non Dirichlet set every proper closed subset of which is Kronecker, A weak Kronecker set which is not an R set; an independent countable Dirichlet set which is not Kronecker; a collection of q-disjoint Kronecker sets whose union is independent but Helson 1/q; A countable collection of disjoint Kronecker sets whose union is closed and independent but not Helson: a perfect independent Dirichlet set which is not Helson.

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     title = {Some results on {Kronecker,} {Dirichlet} and {Helson} sets},
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Korner, Thomas-William. Some results on Kronecker, Dirichlet and Helson sets. Annales de l'Institut Fourier, Tome 20 (1970) no. 2, pp. 219-324. doi : 10.5802/aif.355. http://archive.numdam.org/articles/10.5802/aif.355/

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