Adding small sets to an 𝑁-set

Bukovská, Zuzana; Bukovský, Lev

doi:10.1090/S0002-9939-1995-1285977-5

Adding small sets to an $\textbf {N}$-set
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by Zuzana Bukovská and Lev Bukovský PDF

Proc. Amer. Math. Soc. 123 (1995), 3867-3873 Request permission

Abstract:

Pseudo Dirichlet and N-sets are small sets of reals defined in the theory of trigonometric series. We prove that by adding a set of cardinality smaller than $\mathfrak {p}$ to an N-set one obtains again an N-set. This is a strengthening of Arbault-Erdös’ theorem about adding countable sets to N-sets. A similar result holds true for pseudo Dirichlet sets.

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