Geodesic
Bohr Cluster Points of Sidon Sets
Colloquium Mathematicum, Tome 68 (1995) no. 2, pp. 285-290.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm-68-2-285-290
Keywords: Bohr compactification, Sidon, quasi-independent, dissociate

L. Ramsey 1

1 
@article{10_4064_cm_68_2_285_290,
     author = {L. Ramsey},
     title = {Bohr {Cluster} {Points} of {Sidon} {Sets}},
     journal = {Colloquium Mathematicum},
     pages = {285--290},
     publisher = {mathdoc},
     volume = {68},
     number = {2},
     year = {1995},
     doi = {10.4064/cm-68-2-285-290},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-68-2-285-290/}
}
TY  - JOUR
AU  - L. Ramsey
TI  - Bohr Cluster Points of Sidon Sets
JO  - Colloquium Mathematicum
PY  - 1995
SP  - 285
EP  - 290
VL  - 68
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm-68-2-285-290/
DO  - 10.4064/cm-68-2-285-290
LA  - en
ID  - 10_4064_cm_68_2_285_290
ER  - 
%0 Journal Article
%A L. Ramsey
%T Bohr Cluster Points of Sidon Sets
%J Colloquium Mathematicum
%D 1995
%P 285-290
%V 68
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm-68-2-285-290/
%R 10.4064/cm-68-2-285-290
%G en
%F 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. http://geodesic.mathdoc.fr/articles/10.4064/cm-68-2-285-290/

Cité par Sources :