This note pushes further the discussion by Beresnevich, Guan, Marnat, Ramirez, and
Velani (Adv. Math. 401 (2022), art. id. 108316) about relations between Dirichlet
improvable, badly approximable and singular points by considering Diophantine sets
extending the notion of bad approximability.
Keywords
Diophantine approximation, metric Diophantine
approximation, geometry of numbers