Lacunarity and the Bohr topology
If G is an abelian group, then G# denotes G equipped with the weakest topology that makes every character of G continuous. This is the Bohr topology of G. If G=ℤ, the additive group of the integers and A is a Hadamard set in ℤ, it is shown that: (i) A−A has 0 as its only limit point in ℤ#; (ii) no S...
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| Veröffentlicht in: | Mathematical proceedings of the Cambridge Philosophical Society 1999-01, Vol.126 (1), p.117-137, Article S030500419800317X |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | If G is an abelian group, then G#
denotes G equipped with the weakest topology
that makes every character of G continuous. This is the Bohr topology
of G. If
G=ℤ, the additive group of the integers and A is
a
Hadamard set in ℤ, it is shown that: (i) A−A
has 0 as its only
limit point in ℤ#; (ii) no Sidon subset of A−A
has
a limit point in ℤ#; (iii) A−A
is a
Λ(p) set for all p |
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| ISSN: | 0305-0041 1469-8064 |
| DOI: | 10.1017/S030500419800317X |