The Fourier dimension is not finitely stable
Fredrik Ekstr\"om
TL;DR
This paper investigates the stability properties of the Fourier dimension, demonstrating that it is not generally stable under finite unions and that its stability differs from that of the compact Fourier dimension.
Contribution
It provides new insights into the stability behavior of Fourier dimension, highlighting its limitations and independence from compact Fourier dimension stability.
Findings
Fourier dimension is not finitely stable.
Stability of Fourier dimension is independent from compact Fourier dimension.
Stability issues vary between different pairs of sets.
Abstract
The Fourier dimension is not in general stable under finite unions of sets. Moreover, the stability of the Fourier dimension on particular pairs of sets is independent from the stability of the compact Fourier dimension.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms