Some results on Kronecker, Dirichlet and Helson sets
Annales de l'Institut Fourier, Tome 20 (1970) no. 2, p. 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.
@article{AIF_1970__20_2_219_0,
     author = {Korner, Thomas-William},
     title = {Some results on Kronecker, Dirichlet and Helson sets},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {20},
     number = {2},
     year = {1970},
     pages = {219-324},
     doi = {10.5802/aif.355},
     mrnumber = {44 \#1995},
     zbl = {0196.08403},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_1970__20_2_219_0}
}
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. https://aif.centre-mersenne.org/item/AIF_1970__20_2_219_0/

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