Bohr Cluster Points of Sidon Sets
Colloquium Mathematicum, Tome 68 (1995) no. 2, pp. 285-290
It is a long standing open problem whether Sidon subsets of ℤ can be dense in the Bohr compactification of ℤ ([LR]). Yitzhak Katznelson came closest to resolving the issue with a random process in which almost all sets were Sidon and and almost all sets failed to be dense in the Bohr compactification [K]. This note, which does not resolve this open problem, supplies additional evidence that the problem is delicate: it is proved here that if one has a Sidon set which clusters at even one member of ℤ, one can construct from it another Sidon set which is dense in the Bohr compactification of ℤ. A weaker result holds for quasi-independent and dissociate subsets of ℤ.
@article{10_4064_cm_68_2_285_290,
author = {L. Ramsey},
title = {Bohr {Cluster} {Points} of {Sidon} {Sets}},
journal = {Colloquium Mathematicum},
pages = {285--290},
year = {1995},
volume = {68},
number = {2},
doi = {10.4064/cm-68-2-285-290},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-68-2-285-290/}
}
L. Ramsey. Bohr Cluster Points of Sidon Sets. Colloquium Mathematicum, Tome 68 (1995) no. 2, pp. 285-290. doi: 10.4064/cm-68-2-285-290
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