Bohr Cluster Points of Sidon Sets

• Autorzy: L. Thomas Ramsey
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Bohr compactification; Sidon; quasi-independent; dissociate

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1995
• Tom: 68
• Numer: 2
• Strony: 285-290

Daty

wydano

1995

otrzymano

1993-08-26

poprawiono

1994-07-22

Twórcy

autor

L. Thomas Ramsey

• Mathematics, Keller Hall, 2565 The Mall, Honolulu, Hawaii 96822 U.S.A.

Bibliografia

• [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.