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2003-2004 Cardinality of bases of families of thin sets.
Lev Bukovský
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Real Anal. Exchange 29(1): 147-153 (2003-2004).


We construct a family of Dirichlet sets of cardinality $\mathfrak c$ such that the arithmetic sum of any two members of the family contains an open interval. As a corollary we obtain that every basis of many families of thin sets has cardinality at least $\mathfrak c$. Especially, every basis of any of trigonometric families $\mathcal{D}$, $\mathcal{pD}$, $\mathcal{B}_0$, $\mathcal{N}_0$, $\mathcal{B}$, $\mathcal{N}$, $\mathcal{wD}$ and $\mathcal{A}$ has cardinality at least $\mathfrak c$. Moreover, we construct an increasing tower of pseudo Dirichlet sets of cardinality $\mathfrak t$.


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Lev Bukovský. "Cardinality of bases of families of thin sets.." Real Anal. Exchange 29 (1) 147 - 153, 2003-2004.


Published: 2003-2004
First available in Project Euclid: 9 June 2006

zbMATH: 1060.03069
MathSciNet: MR2061300

Primary: 03E05 , 03E75 , 26A99 , 42A20 , 42A28

Keywords: basis , family of thin sets , tower , trigonometric thin sets

Rights: Copyright © 2003 Michigan State University Press

Vol.29 • No. 1 • 2003-2004
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