# Bohr Cluster Points of Sidon Sets

Colloquium Mathematicae (1995)

- Volume: 68, Issue: 2, page 285-290
- ISSN: 0010-1354

## Access Full Article

top## Abstract

top## How to cite

topRamsey, L.. "Bohr Cluster Points of Sidon Sets." Colloquium Mathematicae 68.2 (1995): 285-290. <http://eudml.org/doc/210312>.

@article{Ramsey1995,

abstract = {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.},

author = {Ramsey, L.},

journal = {Colloquium Mathematicae},

keywords = {Bohr compactification; Sidon; quasi-independent; dissociate; Bohr cluster points; Sidon subsets; random process},

language = {eng},

number = {2},

pages = {285-290},

title = {Bohr Cluster Points of Sidon Sets},

url = {http://eudml.org/doc/210312},

volume = {68},

year = {1995},

}

TY - JOUR

AU - Ramsey, L.

TI - Bohr Cluster Points of Sidon Sets

JO - Colloquium Mathematicae

PY - 1995

VL - 68

IS - 2

SP - 285

EP - 290

AB - 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.

LA - eng

KW - Bohr compactification; Sidon; quasi-independent; dissociate; Bohr cluster points; Sidon subsets; random process

UR - http://eudml.org/doc/210312

ER -

## References

top- [K] Y. Katznelson, Sequences of integers dense in the Bohr group, in: Proc. Roy. Inst. Techn., June 1973, 73-86.
- [LR] J. M. López and K. A. Ross, Sidon Sets, Marcel Dekker, New York, 1975, pp. 19-52.
- [P] G. Pisier, Arithmetic characterization of Sidon sets, Bull. Amer. Math. Soc. 8 (1983), 87-89. Zbl0505.43002

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.