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 set; an independent countable Dirichlet set which is not Kronecker; a collection of -disjoint Kronecker sets whose union is independent but Helson ; 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.
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 ; un ensemble de Dirichlet dénombrable indépendant qui n’est pas un ensemble de Kronecker ; une famille de ensembles de Kronecker disjoints dont l’union est indépendante mais n’est pas un ensemble de Helson ; 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.
@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}, pages = {219--324}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {20}, number = {2}, year = {1970}, doi = {10.5802/aif.355}, mrnumber = {44 #1995}, zbl = {0196.08403}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.355/} }
TY - JOUR AU - Korner, Thomas-William TI - Some results on Kronecker, Dirichlet and Helson sets JO - Annales de l'Institut Fourier PY - 1970 SP - 219 EP - 324 VL - 20 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.355/ DO - 10.5802/aif.355 LA - en ID - AIF_1970__20_2_219_0 ER -
Korner, Thomas-William. Some results on Kronecker, Dirichlet and Helson sets. Annales de l'Institut Fourier, Volume 20 (1970) no. 2, pp. 219-324. doi : 10.5802/aif.355. http://www.numdam.org/articles/10.5802/aif.355/
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