DESCRIPTIVE PROPERTIES OF THE TYPE OF AN IRRATIONAL NUMBER - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

DESCRIPTIVE PROPERTIES OF THE TYPE OF AN IRRATIONAL NUMBER

Résumé

The type τ(α) of an irrational number α measures the extent to which rational numbers can closely approximate α. More precisely, τ(α) is the infimum over those t∈R for which |α−h/k|0. In this paper, we regard the type as a function τ:R\Q→[1,∞] and explore its descriptive properties. We show that τ is invariant under the natural action of GL2(Q) on R\Q. We show that τ is densely onto, and we compute the descriptive complexity of the pre-image of the singletons and of certain intervals. Finally, we show that the function τ is [1,∞]-upper semi-Baire class 1 complete.
Fichier principal
Vignette du fichier
21WORKINGVERSION.pdf (433.81 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04156866 , version 1 (09-07-2023)

Identifiants

Citer

William Banks, Asma Harcharras, Dominique Lecomte. DESCRIPTIVE PROPERTIES OF THE TYPE OF AN IRRATIONAL NUMBER. 2023. ⟨hal-04156866⟩
11 Consultations
10 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More