Remarks on small sets related to trigonometric series
Tomek Bartoszynski, Marion Scheepers
TL;DR
This paper investigates how various classes of sets related to trigonometric series behave under the addition of small-sized sets, revealing closure properties for these classes.
Contribution
It demonstrates that classes such as N_0-sets, Arbault sets, N-sets, and pseudo-Dirichlet sets are closed under the addition of small sets, advancing understanding of their structural properties.
Findings
Several classes of sets are closed under adding small sets
Closure properties are established for N_0-sets, Arbault sets, N-sets, and pseudo-Dirichlet sets
Results contribute to the theory of sets related to trigonometric series
Abstract
We show that several classes of sets, like N_0-sets, Arbault sets, N-sets and pseudo-Dirichlet sets are closed under adding sets of small size.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Harmonic Analysis Research · Approximation Theory and Sequence Spaces